User talk:Trovatore

Previous discussions:

• Archive 1 (1 July 2005 to 13 October 2005):
• Archive 2 (17 October 2005 to 14 February 2006):
• Archive 3 (12 February 2006 to 4 December 2006):
• Archive 4 (5 December 2006 to 13 June 2011, except one thread):

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CH

In response to

By the way, CH actually *is* an open question.

Is that really the way people see it? I'm accustomed to it being treated like the parallel postulate: it depends on what you're doing. The 'existence' of hyperbolic space is not a challenge to the parallel postulate any more than the 'existence' of rectangles is to ~(parallel postulate).

I don't think it's generally accepted that either CH or not-CH is inconsistent (indeed, with Cohen's proof, it's not clear in what sense it could be without much of modern set theory falling apart). Are you suggesting a philosophical position?

(Not an attack, just curious.)

CRGreathouse (t | c) 01:15, 11 June 2011 (UTC)

My philosophical position is that there is no clear line between philosophy and mathematics (or between mathematics and science), so sure, you can call it a philosophical position if you like.

Of course there are models of ZFC satisfying CH, and others satisfying ~CH; up to here you're fine.

But you know, there are also models of ZFC satisfying Con(ZFC), and others satisfying ~Con(ZFC), and we don't treat those on an equal basis. We think Con(ZFC) is true (if it isn't, then there aren't any models of ZFC at all), so the models satisfying Con(ZFC) are right, and the other ones are wrong.

Now, you could make a distinction here on the grounds that both CH and ~CH have wellfounded models, whereas all models of ~Con(ZFC) are illfounded (in fact, they're not even ω-models).

But are the opinions of all wellfounded models equally correct? Surely not. For example, there are wellfounded models that think that 0# does not exist. But if it does exist, which seems like the reasonable thing to believe at this point, then those models are wrong.

I think I'll stop here for the moment; I'm interested to see what you do with the above. --Trovatore (talk) 09:03, 11 June 2011 (UTC)

Frankly I'm not a fan of Regularity (seems like too much assumption for too little 'bang'), so I'm not convinced by the ill-foundedness of ~Con(ZF) models though it supports my feelings in this matter.

It just seems like the claim that CH is open relies on either ZF being false or the system under which the question is to be interpreted changing. The former case seems unlikely; the latter seems unrelated to CH itself.

CRGreathouse (t | c)

The axiom of foundation (that's the more usual name than "regularity") is really not an assumption at all. All it says is that we're restricting attention to the wellfounded sets. Note that illfounded models still satisfy foundation. That is to say, they think they're wellfounded. They just happen to be wrong about that.

I'm sorry, I don't understand your second paragraph at all. --Trovatore (talk) 22:21, 13 June 2011 (UTC)

There is one way in which ~Con(ZF) is different from ~CH — if ~Con(ZF) were true, then we could write down an actual proof of a contradiction from ZF, a complete finitary object. While the best one can do with CH or ~CH is to construct (small) finitary fragments of models of ZFC+CH or of ZFC+~CH. JRSpriggs (talk) 11:44, 14 June 2011 (UTC)

That's a difference, certainly, but I don't see that it's relevant in context. If you take the position that the truth of statements of set theory is relative to models of ZFC, then you have to come to terms with the fact that there are models of ZFC that disagree on the truth value of Con(ZFC). --Trovatore (talk) 16:15, 14 June 2011 (UTC)

Re: LivingBot edit summaries

It is a reference to the preceding sentence ("Revert if in doubt.") Say, for example, you're watching the talk page for "Stretcher" (medical apparatus). Now, LivingBot tags it for a book about woodworking. Clearly, what was meant was Stretcher (piece of wood). The comparison with Georgia is used to imply that LivingBot may actually not be wrong, and you should stop and think before reverting it. - Jarry1250 ^{[Weasel? Discuss.]} 22:02, 19 June 2011 (UTC)

Your indent style

Regarding this change. Your preferred style makes no sense whatsoever. We both replied to the same comment, I replied before you, and you replied after me. Your method is as follows: if someone replies before you, then you insert your reply above their earlier reply with an extra level of indentation. That has two main flaws:

• Your extra level of indentation adds to confusion. (Indent level n is a reply to indent level n–1. Using three indents, when there's only a level zero and level one indent means that you are replying to no-one!)
• You imply that your comment is somehow more important than other people's by "cutting in line".

Why should you insert your reply above mine? I replied first, you replied second, ergo, my reply is placed before yours. Following your reasoning, the person to reply after you, i.e. third, should put their reply above both mine and yours, and with an indent level of four (again, replying to no-one). I'll leave you to think about this. Even though you prefer your anachronistic style, it goes against WP:INDENT, and it's quite simply rude. — Fly by Night (talk) 05:46, 10 July 2011 (UTC)

Come on, FBN, you're making way too much of this. I'm not going to apologize because I don't think I did anything wrong. But I am distressed that it strikes you this way, which I never intended.

To my eye, responses to the same person, indented the same, have a tendency to blend together; the first person's comments get attributed to the second person. I don't have a fixed "style" to solve this problem, but deal with it ad hoc, either with the way I did it, or sometimes by putting an extra newline before my comment. It's silly to extrapolate what would happen if it were iterated; common sense comes into play. --Trovatore (talk) 07:07, 10 July 2011 (UTC)

Boiled Lamb?

In the discussion on Wholemeal starchy food you refer to boiled lamb with mint jelly as, I think, an English food. I'm intrigued and have never come across any method of cooking lamb that involved boiling it. Are you sure you're not thinking of roasted lamb? I'm asking here rather than extend an off-topic conversation on the refdesk. Thanks. --Frumpo (talk) 08:33, 25 July 2011 (UTC)

Could be roasted, don't know. --Trovatore (talk) 10:01, 25 July 2011 (UTC)

The old testament of the Bible mentions "You shall not boil a young goat in its mother’s milk." in Deuteronomy 14:21. I presume that this would not have been mentioned unless that method of preparation was common-place back then. JRSpriggs (talk) 10:46, 25 July 2011 (UTC)

I suppose a lamb stew (typically with carrots and other vegetables) is sort-of boiled lamb but this wouldn't be normally served with mint sauce. Mint sauce (with a vinegar base) is traditionally served with slices of roast lamb. I haven't seen the sweeter mint jelly for several years. I don't much fancy the idea of lamb boiled in milk but it sounds like an interesting preparation. --Frumpo (talk) 20:52, 25 July 2011 (UTC)

Julius Caesar

I've seen many interesting opinions on the chap, but never that he was a "thug".

What makes you think that of him? --Dweller (talk) 09:09, 28 July 2011 (UTC)

He took over Rome by military force, and installed himself as military dictator. I don't know what else you need. --Trovatore (talk) 09:36, 28 July 2011 (UTC)

Dictator in those days doesn't quite mean the same as these. You can't divorce Caesar from the times he lived in... the traditional senatorial system of the Republic was falling apart and someone had to get a grip. It was him, though not for long. if he hadn't, one of the other triumvirs (or someone else) would have dealt with him rather unfavourably. And what followed him was a path into far greater dissolution of senatorial power. I don't think there's much thuggish about his behaviour though - he believed in the rule of law. To me, he comes across as a powerful man, who was a masterful general, perhaps the most masterful of all time, who couldn't quite make the leap to the imperium. His mistake was that he alienated people and perhaps wasn't thuggish enough to deal with them like a real thug, say Saddam Hussein or Stalin, would have done. --Dweller (talk) 10:10, 28 July 2011 (UTC)

I am not an expert on the times, but I have a very low opinion of Julius Caesar. I see him as a mob-pandering military ruler, something like the Hugo Chavez of his day (though of course even Chavez in the current day doesn't use the brutal tactics Caesar did). -Trovatore (talk) 10:26, 28 July 2011 (UTC)

Mob-pandering = popular with the masses? He does seem to have been, but that's not usually a trait of a thug. Caesar's tactics in Rome were spectacularly unbrutal - our article on him notes how he pardoned and spared his opponents. Although he was indeed brutal in warfare against the Gauls and other non-Roman tribes, but you'd expect that of any warrior of his day, and Rome's survival probably depended on it. He also tried to refuse some of the honours the Senate bestowed on him. Give him another look - he's a fascinating and complex character. --Dweller (talk) 11:01, 28 July 2011 (UTC)

The word "dictator" referred originally to an official appointed by the Senate to exercise unlimited powers ("he was not legally liable for official actions") for (up to) one year during an emergency. The word got the bad connotation it has today because of the frequent abuse of that power.
Gaius Julius Caesar was a left-wing military dictator, similar to Hugo Chavez as you say. JRSpriggs (talk) 14:20, 28 July 2011 (UTC)

Logicism

Hi, this may be an odd thing to post, but I don't come around here often and have always found you insightful, so would like to ask your help. The article on Logicism seems to be in a poor state and I don't think the people editing it know what they are talking about (If I'm wrong, I'm very very sorry) Could you take a look at the page (if interested, and if you have time) and give some sort of opinion or indication of a direction it should go in? Finally, I'm the IP address under the small changes section on the talk page there; I'm not asking you to come and agree with/back up what I'm arguing (you may very strongly disagree) all I want is someone who knows what they're talking about to look at it. 71.195.84.120 (talk) 16:16, 31 July 2011 (UTC)

From pure historical fact, the intro looks very accurate up to the early 1900's. Thereafter (failure of Logicism and Formalism to reduce all of Mathematics to simple Mechanism) there's little info to criticise: article is not inaccurate, just incomplete. Bill Wvbailey (talk) 03:07, 1 August 2011 (UTC)

What I was looking for comment on was a debate going on on the talk page about two things I removed. The first, refering to Godel's Theorem being an objection to Logicism:

"However, the basic spirit of logicism remains valid, as that theorem is proved with logic just like other theorems"

The second:

"Today, the bulk of modern mathematics is believed to be reducible to a logical foundation using the axioms of Zermelo-Fraenkel set theory (or one of its extensions, such as ZFC), which has no known inconsistencies (although it remains possible that inconsistencies in it may still be discovered). Thus to some extent Dedekind's project was proved viable, but in the process the theory of sets and mappings came to be regarded as transcending pure logic."

The second removed because, I may be mistaken, I didn't think that mathematics = ZFC was logicism (I'm not asserting this equality) Second, I'm not sure that it is believed that math reduces exactly to ZFC, but more it reduces to Set Theory, which aren't the same. Since what was written didn't seem right, but I wasn't sure exactly what to replace it with, I removed it. I wanted someone else to look at it because some of the comments on the talk page don't seem very informed. I realize that my objections may seem pedantic, but the article seemed to read as pro-logicism to me; and it didn't seem to explain anything about logicism.209.252.235.206 (talk) 03:47, 1 August 2011 (UTC)

Sorry, I didn't have Logicism on my watchlist so I missed the debate. My (historical) take on it is this: Logicism died in ca 1927 2nd edition of PM (see the introduction to that volume), wherein Russell admitted his inability to axiomitize all of mathematics in particular because of the failure of his axiom of reducibility. At this time Hilbert's Formalism, and various "set theories" were in fairly developed stages, and Russell yielded the floor to these theories (with intuitionism a nettlesome bugbear). Russell's axiom was taken up by Goedel in a ca late 1940's important paper, so it's not at all clear that Logicism is strictly "dead". I'm sitting in an airport writing this and when I have more time I'll look deeper at the debate. BillWvbailey (talk) 16:50, 1 August 2011 (UTC)

Walking dead 'eh? First of all, there is a theory called "Neo-logicism" which is thriving just fine. I suppose we could get hyper-semantic and just say something like '...neo-logicism isn't anything like logicism ... it's totally different.' Which is exactly the type of response I expect. However, that would be disingenuous. The idea is that everything in mathematics can be reduced to some logical truth. This claim is eminently reasonable as every mathematician always wants to be logical, and every mathematician always wants to express truths. To the degree that mathematicians run away from logicism, they deserve to lose their credibility. The approach that neo-logicism takes is to expand what we mean by "logic." This, is a perfectly legitimate way to deal with things, and is only at most an equally semantic approach to the approach that the mathematicians are taking in running away from logicism. (Um, who was it who said -- ridiculously -- on a WP talk page that "mathematical logic isn't logic?") Interestingly, the "walking dead" came out with something JUST TODAY.

It's my own person understanding that so-called "philosophical" logicians will always reasonably be able to expand what we mean by "logic" as our knowledge increases. Therefore we will always be able to construct a valid interpretation under which some form of logicism is true. This is their proper role. It is also more properly their role to say whether semantic claims such as "mathematical logic isn't logic" are valid or not. It is not the proper role of a mathematician. Who do you ask about soil, a soil scientist or an archeologist? Greg Bard (talk) 23:04, 1 August 2011 (UTC)

How is that reasonable exactly? You will always be able to expand what you mean by Logic so that some form of Logicism will be true? Assume I'm stupid and need helped through that because it sounds, to me, like you are saying logic can be what ever you need it to be.

Now for the other matter: Most of my complaining on the talk page is from pairs of sentences like these:

"The idea is that everything in mathematics can be reduced to some logical truth. This claim is eminently reasonable as every mathematician always wants to be logical, and every mathematician always wants to express truths."

Those are not saying the same thing! Saying that all of mathematics (again, the philosophical total form of the word, not just all the math we can do now, but literally everything it can ever be) can be reduced to logic is not the same concept as saying that mathematicians want to be logical in their approach and aspire to truth. You know what? Physicists also want to be logical and aspire to truth, is all of empirical science now also reducible to logic? Obviously not. Just because mathematicians use logic does not mean that everything is logic. 209.252.235.206 (talk) 07:34, 2 August 2011 (UTC)

The problem is that you are confusing philosophy with psychology. When I say that every mathematician wants to always be "logical," I am not meaning 'spock-like' or some other such notion. I mean it in precisely the sense that the context makes obvious. I.e. the actions of the mathematician when he or she scribbles an expression on the chalkboard are the product of reason. More specifically, there always exists some logical system with some interpretation in which the scribbles can be validly constructed. Yes they are saying the same thing. We are able to expand what we mean by logic in the exact same way that every other academic field does exactly the same thing. We make new discoveries and they are published in academic journals. Do not get the wrong idea. I am not talking about a semantic difference of which academic departments choose to focus on which concepts. I am talking about new discoveries in the field of logic which are consistent with the principles of logic in reality.

I am a little surprised by the issues that you have brought up due to what appears to me to be fairly obvious. Please forgive that. Your counter-example of physics I find to be quite off. Obviously, physics involves an empirical component, while logic does not. Therefore there is no "reducing" all of physics to logic, much less "everything." Math however, does not escape that reduction. The degree to which physics "reduces" to logic is in that the scribblings of a physicist are an interpretation (or model) of the physical world we live in. I.e. they are attempts to formalize the principles of the empirical sciences. The aim of these attempts is to construct a formal system that will produce all of the theoretical possibilities (preferably in the end they are in the form of true sentences) and none of the impossibilities. I don't see how math can escape such a treatment, with the notable exception that math has no empirical component, and therefore reduces to logic just fine.

I also wonder what the problem is with logic being 'whatever you need it to be.' I am pretty sure Wittgenstein famously described logic as being like a ladder that you can climb and then throw away. We have non-standard logic, non-classical, etcetera. To say that logic is whatever you need it to be also sounds eminently reasonable. Math also appears to be 'whatever you want it to be...' you have graph theory, arithmetic, game theory, topology. Greg Bard (talk) 22:14, 12 August 2011 (UTC)

--

I'm unfamiliar with "neologicism". I'm only discussing "logicism" here, as it is used in the literature (see the following quotes). Here's what Kleene wrote:

"The logicistic thesis can be questioned finally on the ground that logic already presupposies mathematical ideas in its formulation. In the intuitionistic view, an essential mathematical kernel is contained in the idea of iteration, which must be used e.g. in describing the hierarchy of types or the notion of a deduction from given premises. || Recent work in the logicistic school is that of Quine 1940. A critical but sympathetic discussion of the logicistic order of ideas is given by Goedel 1944." (Kleene 1952:46)

Here's what Eves wrote (notice that he seems to have borrowed from Kleene !): "Whether or not the logistic thesis has been established seems to be a matter of opinion. Although some accept the program as satisfactory, others have found many objections to it. For one thing the logistic thesis can be questioned on the ground that the systematic development of logic (as of any organized study) presupposes mathematical ideas in its formulation, sucah as the fundamental ideas of iteration that must be used, for example, in describing the theory of types or the idea of deduction from given premises." (Eves 1990:268).

In the latest Scientific American article there's an article by Mario Livio "Why Math Works" wherein he discusses two -isms only: Formalism and Platonism (August 2011:81) and tries to answer the question about whether mathematics is intrinsic to the universe and discovered by mankind (Platonism), or whether it is Formalistic in nature -- i.e. invented by mankind. He concludes both seem to be the case.

This brings me to a final thought (opinion) that what we have in this discussion is of confusion between philosophy of mathematics (Formalism and Platonism) and a particular practice of mathematics (Logicism). I personally am sympathetic to the Kleene-Eves point of view (Logicism is a failure) and I agree with Livio who is also a bit perplexed by this universe of ours: "Why are there universal laws of nature at all? Or equivalently: Why is our universe goverened by certain symmetries and by locality? I truly do not know the answers . . ." (p. 83). At least now we have a few quotes from reputable writers to apply to the issue. I'll keep hunting for more. Bill Wvbailey (talk) 13:37, 2 August 2011 (UTC)

I found a great quote that corroborates my opinion about Logicism being a "practice" rather than a philosophy. This is from Brouwer's 1907 The Foundations as quoted by Mancosu 1998:9 -- " 'The Foundations' (B1907) defines "theoretical logic" as an application of mathematics, the result of the "mathematical viewing" of a mathematical record, seeing a certain regularity in the symbolic representation: "People who want to view everything mathematically have done this also with the languarge of mathematics . . .the resulting science is theoretical logic . . . an empirical science and an application of mathematics . . . to be classed under ethnography rather than psychology" (p. 129) || The classacial laws or principles of logic are part of this observed regularity; they are derived from the post factum record of mathematical constructions. To interpret an instance of "lawlike behavior" in a genuine mathematical account as an application of logic or logical principles is "like considering the human body to be an application of the cience of anatomy" (p. 130).

(But I ask: why do we humans view the universe's apparently regularity? Is it because of an intrinsic "logical" design of our brains?) There's more to be found in Grattain-Guinness:2000 (about 35 cites in his index). Bill Wvbailey (talk) 14:09, 2 August 2011 (UTC)

To Gregbard: There are some people who purport to be mathematicians or logicians who are not logical. See "synthetic logic", "fuzzy logic", "Paraconsistent logic", and their ilk.

You said "math has no empirical component". This is false. Mathematics, including logic, is just as empirical as nuclear physics or chemistry. Any calculation or deduction done by a mathematician is actually done in the physical world by some sequence of operations on matter. If these operations did not produce what we consider the proper result, then either that mathematics would not exist or it would be different from what we know it to be. JRSpriggs (talk) 03:57, 13 August 2011 (UTC)

Aye aye aye. Your characterization of these other mathematicians as "not logical" is just your characterization of them. These people are not setting out to ignore or abandon reason, but rather have constructed a different model of what is reason. Invariably they point to reasons for their constructions. Anyway, the focus should be on the systems, not the people. I think you intend to claim that the systems of logic these people construct are "not logical." Like I said this isn't psychology. Whether or not logic is empirical is a very deep and complex subject, and it is not universally agreed that it is empirical. The prevailing view is the opposite. Your appeal to physicalism has my sympathy, as I am a physicalist as well, however physicalism is a metaphysical theory addressing whether or not there is a dualism between mind and matter. The question of whether logic is empirical is not effected by anyone's metaphysical physicalist or idealist views. Empiricism involves being experienced by the senses. Exactly what sense are you using to sense that a particular truth of mathematics is true? It couldn't be sight, after all, a person could conceivably discover all the truths of logic and mathematics sitting alone with eyes closed. <or>I think more properly that like there is evolution in response to the environment, and so too, the evolution of the brain is a response to the 'logical environment' of this universe.</or> As a physicalist, I would say that the 'logical environment' is only experienced through particular instances of activity involving physical matter. However to say that what I am calling the 'logical environment' itself is physical or in anyway directly sensed through the five senses would need some justification and explanation. You only experience it indirectly which makes the "empirical" logic and mathematics of your view only a soft science. Is that your view? That mathematics is empirical, and that it is a soft science? Who is the psychologist now? In my view, we can call things like a "sense of reason", or a "sense of decency" senses, however, they really are a different category of thing than the five senses, and not empirical. Saying that mathematics is done in the physical world does not make mathematics empirical, otherwise astrology, religion, and "noetic science" would also equally be empirical. Greg Bard (talk) 11:25, 13 August 2011 (UTC)

Supposition on evenness of zero misunderstanding

Hi Trovatore. As Wikipedia:Reference_desk/Archives/Mathematics/2011 August 10#Is zero really an even number? will soon be archived, I wanted to point out my suppositional response to you question. -- 110.49.248.124 (talk) 15:32, 15 August 2011 (UTC)

Composite numbers have at least three (but finitely many) non-negative divisors. Prime numbers have two non-negative divisors. One has one non-negative divisor. So in some sense, one is too prime to be merely prime; instead, it is the multiplicative identity. Zero, on the other hand, has an infinite number of non-negative divisors (too composite to be merely composite). JRSpriggs (talk) 23:15, 15 August 2011 (UTC)

Infinite Dimensional Spaces

Hello Sir. Regarding this question on the maths reference desk. It seems that it's defined the way that it is so that it's a CW complex. You gave a lot of input and really tried to help (which I appreciate), and so I thought you might like to know. All the best. — Fly by Night (talk) 01:55, 21 August 2011 (UTC)

capitalization

If you'll look at the bottom of Wikipedia talk:Manual of Style (capital letters)‎, you'll see that I linked the guideline modification that includes the example "Halley's comet" and mentions astronomical objects. Both Halley's comet and Andromeda galaxy are quite commonly lowercased in sources. I'm attempting to attract a bit more discussion, so just reverting and saying in the edit summary that you missed the discussion isn't all that helpful. Dicklyon (talk) 06:17, 27 August 2011 (UTC)

I find your recent editing frankly disingenuous. The (talk page) section you mention does not mention celestial bodies at all. You can't take a couple of people vaguely agreeing with a general sentiment as a mandate to impose such a change. Much much worse was that you then, one minute later, used your change as the basis for a requested move at Halley's Comet, without mentioning that it was your change. You really overstepped the line here, badly. --Trovatore (talk) 06:21, 27 August 2011 (UTC)

The change is an attempt to clarify WP's "don't overcapitalize" style. The section is linked in the talk page, and I'm inviting your input there. The RM is already well enough supported by COMMONNAME among other things, since Halley's comet has long been traditionally rendered in lower case, and still is about 50%, as are other well-known comets like comet Hale–Bopp. Dicklyon (talk) 06:39, 27 August 2011 (UTC)

That may all be true. It's not the point. You didn't discuss the specific change to the celestial bodies section, in specific terms, before making the change. Then, having unilaterally made the change, you used it in support of your position for the requested move.

That just looks dishonest. I am not saying you personally are a dishonest person, and you may have just been careless about assuming that others had approved the intermediate steps. I can't read your mind; I can see only the edits, and to me they look dishonest, however you may have intended them.

I haven't contributed on the merits because I have nothing particular to say about the merits. I don't really care whether comet is capitalized or not. --Trovatore (talk) 07:32, 27 August 2011 (UTC)

I certainly wasn't trying to hide anything, but to attract some discussion. The guideline, not necessarily the example that I changed, is what I'm relying on. Dicklyon (talk) 07:40, 27 August 2011 (UTC)

OK, I can buy that. But surely you must realize that the MoS is full of special cases that may be in tension with general principles. Whether it should be or not, it is. So I'd invite you to be more cautious about making changes to specifics when relying on the generalities, without consensus that they apply and are not covered by an exception.

As to the specific changes to the "celestial bodies" section, those examples did not make sense anymore after your change. The section said you should capitalize names of celestial bodies, but you changed it to capitalize only the parts that would have been capitalized in any case because of being names of real or fictitious persons. A better example might be the Coal Sack Nebula, however we should or shouldn't capitalize that, a question on which I claim no expertise (though all three words uppercase looks most natural to me, for whatever that's worth). --Trovatore (talk) 08:19, 27 August 2011 (UTC)

August 2009

You currently appear to be engaged in an edit war according to the reverts you have made on Wikipedia:Manual_of_Style_(capital_letters). Users are expected to collaborate with others and avoid editing disruptively.

In particular, the three-revert rule states that:

1. Making more than three reversions on a single page within a 24-hour period is almost always grounds for an immediate block.
2. Do not edit war even if you believe you are right.

If you find yourself in an editing dispute, use the article's talk page to discuss controversial changes; work towards a version that represents consensus among editors. You can post a request for help at an appropriate noticeboard or seek dispute resolution. In some cases it may be appropriate to request temporary page protection. If you continue to edit war, you may be blocked from editing without further notice. --Enric Naval (talk) 18:33, 27 August 2011 (UTC)

Enric is a day late (or two years late) and couple of reverts short, since we already stopped reverting and talked about it. Unclear why he decided to be so obnoxious at this point. Dicklyon (talk) 18:39, 27 August 2011 (UTC)

You'll notice that I made a recent step toward a less controversial version; let me know what you think. Dicklyon (talk) 18:40, 27 August 2011 (UTC)

Wikipedia:Administrators'_noticeboard/Edit_warring#User:Dicklyon_reported_by_User:Enric_Naval_.28Result:_.29. --Enric Naval (talk) 20:41, 27 August 2011 (UTC)

File:Unif small.jpg listed for deletion

A file that you uploaded or altered, File:Unif small.jpg, has been listed at Wikipedia:Files for deletion. Please see the discussion to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. Sven Manguard Wha? 03:39, 30 August 2011 (UTC)

File:Unif.png listed for deletion

A file that you uploaded or altered, File:Unif.png, has been listed at Wikipedia:Files for deletion. Please see the discussion to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. Sven Manguard Wha? 03:40, 30 August 2011 (UTC)

re: Edit at refdesk

It certainly was an accident. I'm not actually sure how that happened --- your reply didn't exist when I began replying, and I wasn't taken to an edit conflict page as I should have been.--Antendren (talk) 23:15, 16 September 2011 (UTC)

Yeah, that happens sometimes. Sorry I overreacted. --Trovatore (talk) 00:50, 17 September 2011 (UTC)

Real zero and integer zero

Hi Trovatore. I am trying to understand your way of doing math. You distinguish between real zero, $0_{R}\,$, and integer zero, $0_{Z}\,$. They are 'completely different breeds of cat', so $0_{R}\neq 0_{Z}\,$, but when they are together in expressions the $0_{Z}\,$ may be converted to $0_{R}\,$ such that for instance $0_{R}+0_{Z}=0_{R}\,$. Do I get it right? The meaning of the power $0^{0}\,$ depend on which one of the zeroes is in play in the exponent such that $0^{0_{Z}}=1$ while $0^{0_{R}}$ is an undefined indeterminate form. Right?. Now what about the rational zero $0_{Q}\,$ ? It is a different breed of cat than $0_{Z}\,$ and $0_{R}\,$. Right? Is $0^{0_{Q}}$ defined to be one or is it undefined? And why? Bo Jacoby (talk) 09:55, 18 September 2011 (UTC).

Bo, most of the time, I don't distinguish between them, because most of the time there's no reason to. I don't want to waste my time making distinctions when they don't make a difference.

But in contexts where they could make a difference, like the famigerated 0^0 thing, I don't think the claim "they're equal, so you can't make a distinction" is really very convincing. You keep saying what disasters would befall, but you've never given a good example, and indeed the fact that these objects are coded differently into set theory, and yet the sky has not fallen, seems to me a pretty convincing demonstration that there is at least no simple disaster that the distinction causes.

As for the rationals, yes, I do think a distinction can still be made. At a sound-bite level, you could say the rationals are inherently algebraic, whereas the reals are inherently topological. As long as you're at the level of algebra, 0^0=1 seems pretty convincing. Add topology and it no longer is. --Trovatore (talk) 23:07, 18 September 2011 (UTC)

Which article you are two discussing? JRSpriggs (talk) 00:38, 19 September 2011 (UTC)

JRSpriggs, Thank you for asking. Trovatore and I had a discussion on Talk:Exponentiation and the archives pages such as Talk:Exponentiation/Archive_3#0.5E0 regarding the definition of 0⁰. Sorry for not being explicit about it here. Bo Jacoby (talk) 02:49, 19 September 2011 (UTC).

Thank you. JRSpriggs (talk) 06:55, 19 September 2011 (UTC)

Trovatore. To a mathematician a contradiction marks the end of civilization as we know it. As both $0_{R}\,$ and $0_{Z}\,$ satisfy the equation of first degree $x+0_{R}=0_{R}\,$ , and actually any equation of the form $x+a=a\,$ , it follows that $0_{R}=0_{Z}\,$ in contradiction to $0_{R}\neq 0_{Z}\,$. This is a simple disaster that the distinction causes. The sky has fallen. The various codings of integers and reals in set theory are merely proofs that the defining axioms for reals and integers are consistent. These codings do not define reals or integers. The axioms do. Bo Jacoby (talk) 08:19, 19 September 2011 (UTC).

Axioms do not define anything. Axioms assume that objects behave in a certain way. From those assumptions you prove other things. --Trovatore (talk) 08:33, 19 September 2011 (UTC)

Now, as to your specific example. The sentence $(\forall x)x+0=x$ is satisfied by the structure $(Z,0,+,\cdot )$ and also by the structure $(R,0,+,\cdot )$. However that does not tell you anything about how the interpretation of the constant symbol 0 in the first structure sits in the second structure. You cannot conclude that $0^{Z}+0^{R}=0^{Z}$, because you don't know that $0^{Z}$ is in element of the universe of the second structure in the first place. --Trovatore (talk) 08:38, 19 September 2011 (UTC)

What does the structures $(Z,0,+,\cdot )$ and $(R,0,+,\cdot )$ mean? Bo Jacoby (talk) 16:38, 19 September 2011 (UTC).

I am sure he means Structure (mathematical logic). Note that, in the usual definitions, $0_{Z}$ is a set of pairs of natural numbers, as is every other integer, while $0_{R}$ is a set of Cauchy sequences of rationals, and so in particular $0_{Z}$ is not a real number and $0_{R}$ is not an integer. It is true that there is an embedding of one structure into another, but this embedding is not the identity. This is completely analogous to the situation in a programming language where there is a type Integer and a type Real, and an object of Integer type has to be cast into the Real type before being passed to a function that takes an argument of type Real. — Carl (CBM · talk) 16:58, 19 September 2011 (UTC)

To put it less technically, your equation $x+0=x$, as interpreted in the real numbers, doesn't tell you anything except in the case that x is a real number. It does not say, for example, that if you add the 0 of the real numbers to me you get back me, because I am not a real number I am a free man. Also, the symbol + is to be interpreted as in the real numbers and there is no guarantee that that has anything to do with the + of any other structure, such as the integers. --Trovatore (talk) 19:12, 19 September 2011 (UTC)

The zeroes in $(Z,0,+,\cdot )$ and $(R,0,+,\cdot )$ confuses me. Did you mean $(Z,+,\cdot )$ and $(R,+,\cdot )$ ? Bo Jacoby (talk) 23:34, 19 September 2011 (UTC).

Structures are specified by a universe and an interpretation. Interpretations tell you how to interpret the constant symbols, function symbols, and relation symbols of the language. Typically, when the way the symbols are to be interpreted is understood from context, you just list which symbols you want to interpret. So I listed the constant symbol 0, and the function symbols plus and times.

I could also have listed the constant symbol 1; that would probably have been more standard. On the other hand 1 is definable in both structures so I didn't really need to list it, but the same is true for 0.

So sure, your suggestion would work, but so would $(Z,0,1,+,\cdot )$ and $(R,0,1,+,\cdot )$, and the latter would probably be more standard. --Trovatore (talk) 23:39, 19 September 2011 (UTC)

Thanks to Carl for the link to Structure (mathematical logic) which I find interesting but difficult to understand in detail.

The same structure can be constructed in different ways. The structure of the real numbers was constructed by Cantor and by Dedekind as completely different breeds of cat. Does this mean that $0_{Cantor}$ is different from $0_{Dedekind}$ ? Or is the important things that they represent different realization of exactly the same structure ?

Trovatore said: ' I don't distinguish between them, because most of the time there's no reason to. I don't want to waste my time making distinctions when they don't make a difference.' I could not agree more! The undefining of $0^{0_{Z}}=1$ into $0^{0_{R}}$ being an indeterminate form is the only example I know of undefining in math. Are there other examples?

(The order of the real numbers is not generalized into the realm of complex numbers, but that does not mean that the order of reals becomes undefined.) Bo Jacoby (talk) 13:14, 20 September 2011 (UTC).

Reply +

I put some stuff for you on my talk page in the section you started, unrelated to the section topic. PPdd (talk) 03:29, 26 September 2011 (UTC)

Reply

Hello. Just to let you know, in case you don't see it any time soon, that I responded to your last comment, on the Talk page. You can click here. Hashem sfarim (talk) 16:22, 5 October 2011 (UTC)

Over-linking, under-linking, and just-right-linking

Trovatore, there seems to be a movement afoot to reduce overlinking by making rules to favor links' role as definers of unfamiliar terms and end their role as pointers to different but strongly related topics—for example, saying that a page about a bureau of immigration shouldn't link to Immigration, because everyone knows what immigration is, and Immigration doesn't provide facts of immediate relevance to the bureau. That sounded like progress to me at first, but as I have seen it play out in practice, it has begun to sit ill with me. Would you be willing to have a look at Wikipedia_talk:MOSLINK and see what you think? —Ben Kovitz (talk) 11:41, 16 October 2011 (UTC)

Ch and ON != OR

These are the same principals... so you were like 1-4 steps from solving CH... that's basically the point of my summary of the proof.

You either chose N_0 to be the first choice, and name the first player 0_R, and the laster player R_e, and then all the information is encoded into the players names and the game... so there is no perfect information since no player knows all the names.

I hope this makes sense to you and you see where I went with it.

-Vince

WhatisFGH (talk) 01:41, 19 October 2011 (UTC)

You know, when I was a grad student I would take up these arguments, but it's gotten old. Why don't you get onto Usenet and post this to sci.logic? I'm sure there'll be people there who are willing to talk about it. http://groups.google.com/group/sci.logic/topics . --Trovatore (talk) 01:45, 19 October 2011 (UTC)

New Page Patrol survey

New page patrol – Survey Invitation Hello Trovatore! The WMF is currently developing new tools to make new page patrolling much easier. Whether you  have patrolled many pages or only a few, we now need to  know about your experience. The survey takes only 6 minutes, and the information you provide will not be shared with third parties other than to assist us in analyzing the results of the survey; the WMF will not use the information to identify you. If this invitation  also appears on other accounts you  may  have, please complete the  survey  once only.  If this has been sent to you in error and you have never patrolled new pages, please ignore it. Please click HERE to take part. Many thanks in advance for providing this essential feedback. You are receiving this invitation because you  have patrolled new pages. For more information, please see NPP Survey. Global message delivery 13:42, 26 October 2011 (UTC)

Another editor correcting your erroneous postings on Ref Desk

I have opened a discussion thread about the modification of the Ref Desk posts of others at Wikipedia talk:Reference desk#Modifying someone else's post. Your input is most welcome. Edison (talk) 06:50, 16 November 2011 (UTC)

Trovatore, just thought I'd drop you a note. I really meant no harm with fixing the link that started the above mentioned thread. I hope no offense was taken, none was intended. I really didn't think such a trivial fix would generate this much drama, but I will definitely be keeping it in mind in the future. Regards, Heiro 14:08, 16 November 2011 (UTC)

No worries. I wasn't offended. --Trovatore (talk) 20:22, 16 November 2011 (UTC)

Physical Turing machines are at best a metaphor

Hi, regarding your posting on the Ref Desk at Wikipedia:Reference desk/Science#Is Wikipedia a conscious entity?, you said that a programmable calculator is not Turing-complete, and that a TM is a mathematical object. Obviously, using a mathematical construct to describe a physical machine is an approximation - namely that physical machines do not have access to the infinite-length-infinite-storage resources of the mathematical structure. Nevertheless, this should be obvious when one talks about physical machines, which was what computational theory was built to address anyway (like why a system of assembly-line beltways, a queue machine, can't handle certain instructions). So unless I'm missing something, I think the statement that calling a programmable computer Turing-complete is "at best a metaphor" is a quite a mischaracterization. Please let me know. SamuelRiv (talk) 22:06, 3 December 2011 (UTC)

People need to be careful throwing around terms like the Church–Turing thesis, which is a concept from mathematical logic, not from the theory of (physical) computation. I stand by my statement. Turing machines are objects treated in mathematical logic; no real-world machine is a Turing machine, and the concept of "Turing completeness" applies only to the idealization of what the machine is supposed to do; it's a misapplication of the concept to talk about any physical machine actually being Turing complete. --Trovatore (talk) 22:55, 3 December 2011 (UTC)

Except it's useful, if discussed properly. I agree that the previous posts were a bit out there, and one shouldn't throw around vocabulary like Church-Turing (or especially, god forbid, Godel's Incompleteness Theorem) without mathematical reason. But saying something is a Turing-complete is useful, like in the assembly line example I gave. If one wants to put some kind of quality-checking machinery into an assembly line, one has to make sure that if the program is too "complex", one knows to make the necessary adjustments to the architecture.

It is relevant in the discussion of quantum computers. We do not and will not have infinite qubits, but because we deal with scaling problems, it is often necessary to know what the complexity class of one's architecture would generalize to. It is also relevant in the discussion of neuroscience, mostly to make sure people don't confuse brain complexity with computational complexity.

So the point is that while I agree that one has to be extremely careful about throwing around mathematics terms (as we are so often reminded in physics), the work of Turing, Church, etc. was inspired to be applicable to the world. A term, then, can be used to make a point with the (hopefully) obvious assumption that it is an abstraction of that term. SamuelRiv (talk) 00:06, 5 December 2011 (UTC)

Well, it's not so much that it's an abstraction of the term, as it is a direct application of the term, but to an idealization of the device. But you have to keep in mind that results that apply to the idealization of the device may not apply to the device itself. This is particularly true for "Turing completeness", which I think is totally out of place to bring in when discussing consciousness. --Trovatore (talk) 00:23, 5 December 2011 (UTC)

Agree with Trovatore. "Turing completeness" is neither necessary nor sufficient for consciousness. Of this I am 100% certain: consciousness has nothing whatever to do with Turing completeness. While I hold that the squirrels on my deck looking for birdseed are in the absolute sense conscious, not a one of them is Turing complete or even a dimly-finite approximation to it -- how many squirrels do you know that can multiply 7 x 5, or even count to three for that matter? Why on earth would a squirrel need to be able to count or multiply? Life and survival and consciousness in this world of ours has nothing whatever to do with Turing completeness, or computation for that matter. Bill Wvbailey (talk) 02:11, 5 December 2011 (UTC)

See Hard problem of consciousness. It's a stub, not an article, really. But the intro gets pretty close to an expression of "the problem". Naively the problem gets its name from the difficulty of "explaining consciousness", but the real source of its moniker is the fact that the question/problem itself is so hard to frame, to grasp, to intuit, to describe/express. Bill Wvbailey (talk) 02:32, 5 December 2011 (UTC)

Transfinite induction

I've started a discussion on the talk page. I will add the sentence back if you do not respond soon and justify yourself. Thehotelambush (talk) 00:40, 8 December 2011 (UTC)

Typesetting Mathematics

Hi Trovatore I want to ask you for help with typesetting mathematics. I am attempting to typeset a summation with a multiline subscript (In this particular example its a summation operator with a n=0 subscript and below that n odd). Usually when using LateX I would make use of the \substack command, but Wikipedia can't parse this command for some reason. Do you know how to do this? I thank you in advance for your help. NereusAJ (talk) 02:40, 23 December 2011 (UTC)

The LaTeX engine used here is kind of restricted. If something doesn't work, in my experience, usually you just have to do without it. In this case I'd suggest just putting the two conditions on one line: $\sum _{n\geq 0,n{\textrm {~odd}}}f(n)$. I know it's ugly.

You could ask Michael Hardy, who sometimes knows more about this stuff. --Trovatore (talk) 03:48, 23 December 2011 (UTC)

Thank you. NereusAJ (talk) 04:13, 23 December 2011 (UTC)

Hi Trovatore. I consulted Michael Hardy. He uses \smallmatrix. For example, \sum_{\begin{smallmatrix} i \ge 0 \\ i\ne 6 \end{smallmatrix}}. — Preceding unsigned comment added by NereusAJ (talk • contribs) 08:12, 25 December 2011 (UTC)

Enumerative combinatorics article

Hi Trovatore. I am busy expanding a stub article on Enumerative combinatorics. I would appreciate your input as I haven't made anything but minor edit so far to Wikipedia. I have added new content to the page and would like your opinion as to my approach. My plans to further expand the article include adding additional examples of combinatorial objects (like Dycke paths, Cayley trees, cycles and permutations) and how these can be enumerated. However, the method for all of them is somewhat similar and I am worried about being repetitive. Thank you. --NereusAJ (T | C) 02:57, 5 January 2012 (UTC)

San Francisco meetup at WMF headquarters

Hi Trovatore,

I just wanted to give you a heads-up about the next wiki-meetup happening in SF. It'll be located at our very own Wikimedia Foundation offices, and we'd love it if some local editors who are new to the meetup scene came and got some free lunch with us :) Please sign up on the meetup page if you're interested in attending, and I hope to see you soon! Maryana (WMF) (talk) 00:31, 10 January 2012 (UTC)

The car's boot???

Hi, there! It's just not English. Possessive 's is not used for inanimate objects. See Thomson & Martinet, A Practical English Grammar 2nd edition (London: OUP, 1976), p. 11, 11c: "When the possessor is a thing of is normally used: the walls of the town ... the legs of the table ... But with many well-known combinations it is usual to put the two nouns together using the first noun as a sort of adjective ... hall door ... dining-room table ... street lamp".

What this means is that it is OK to say "the boot of the car" and OK to say "the car boot", as in the common phrase "car boot sale". But it is absolutely not OK to say "the car's boot". It is a comical error that would be red-pencilled in primary school. That it is uncorrected in the MOS is ... well, unbelievable. Best regards, Justlettersandnumbers (talk) 00:26, 10 February 2012 (UTC)

I think you're just flat wrong. This is completely standard English. I have never heard of Thomson & Martinet but it must be a very odd book. --Trovatore (talk) 00:36, 10 February 2012 (UTC)

Let me hazard a guess: you are not a native speaker of British English. That's not a crime. But if the MOS wants an example of how to translate from one idiom to the other, it'd better get both of them right, wouldn't you say? If you don't know that particular – and rather well-known – standard grammar, would you refer me to another grammar of British English that supports your position? Or otherwise consider undoing your reversion of my edit? Justlettersandnumbers (talk) 00:54, 10 February 2012 (UTC)

Thank you. If people want to spend time looking for a better example, I'm ready & willing to participate. Meanwhile, Evviva Verdi! Justlettersandnumbers (talk) 01:21, 10 February 2012 (UTC)

You know, I actually don't see anything in the passage you quote that says it's an error to say the car's boot. Depending on the context in which the passage occurs, it may suggest that the boot of the car is more usual, but that is a rather different thing.

To me the difference between the car boot and the car's boot would be that, in the second form, you have a particular car in mind, whereas when car is used appositively it's more explaining what sort of boot it is (for example, that it's not footwear). --Trovatore (talk) 01:46, 10 February 2012 (UTC)

Just for reference, a few examples of possessives on inanimate objects in British English: car's car's car's car's car's phone's show's palace's region's century's. — Carl (CBM · talk) 02:05, 10 February 2012 (UTC)

I can only assume that Thomson & Martinet were trying to apply a particular bugbear of their own: it was certainly not descriptive. Their book's assertion is not in keeping with British English's normal practice. Kevin McE (talk) 07:24, 10 February 2012 (UTC)

Well, as I said above, I don't even see it in the quote from T&M. It does say that of is "normally" used, an assertion I won't disagree with (even in American English), but that's very different from saying that the possessive form is an error, or even something to be preferentially avoided. --Trovatore (talk) 07:29, 10 February 2012 (UTC)

I don't know of any inhibition against possessives of things in American English, either. I have lots of guides, haven't seen anything like that. In book search, I did find one guide that says use "of", but also says that nowadays its increasingly common to just use the possessive apostrophe. It also has a completely lame example: "pile of coats" as opposed to "coat's pile", which is not a possessive at all so nobody would do that. Like a "coal's lump"? Dicklyon (talk) 08:02, 10 February 2012 (UTC)

Hi Trovatore, long time. I should probably not reopen this old thing, but I have the itch. Thomson and Martinet are quite correct to say *But with many well-known combinations it is usual to put the two nouns together using the first noun as a sort of adjective* and economy of language makes this mode of expression attractive - but here it is no longer a possessive but an attributive and this kind of construction is not flexible enough to serve as a general replacement for possessives. For example, consider "The office's east-facing windows" or "the dog's most chewed bone" - the attributive equivalent rearrangement is ungrammatical and the "of" construction does not improve the passage. And the attributive construction also needs to be idiomatic: e.g., the NPs in "through ill-use the trousers suffered three rents and the jacket two" could be referred to again as "the trouser's holes", but "the trouser holes" is unidiomatic, sounding as if they are holes that trousers are expected to have.

This is an example of a poorly understood recommendation being oversimplified and hardened into peevological dogma. I do hope those primary school teachers aren't for real. — Charles Stewart (talk) 10:32, 26 October 2012 (UTC)

Stefan–Boltzmann law qn in ref desk

Can you help me answer things in the "Stefan–Boltzmann law" section in the reference desk? It is above the absolute temperature section.Pendragon5 (talk) 00:22, 12 February 2012 (UTC)

Mary Surratt

Wow. BusterD (talk) 21:17, 31 March 2012 (UTC)

Nomination of Tautology (rhetoric) for deletion

A discussion is taking place as to whether the article Tautology (rhetoric) is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted.

The article will be discussed at Wikipedia:Articles for deletion/Tautology (rhetoric) (2nd nomination) until a consensus is reached, and anyone is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on good quality evidence, and our policies and guidelines.

Users may edit the article during the discussion, including to improve the article to address concerns raised in the discussion. However, do not remove the article-for-deletion template from the top of the article. Ten Pound Hammer • ^{(What did I screw up now?)} 01:11, 1 April 2012 (UTC)

File:WPMozillaBug.png listed for deletion

A file that you uploaded or altered, File:WPMozillaBug.png, has been listed at Wikipedia:Files for deletion. Please see the discussion to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. Cloudbound (talk) 21:26, 8 April 2012 (UTC)

Impossible colors

Trovatore, Your answer about red+green could easily be misinterpreted as "additive and subtractive color mixing are really more or less the same thing, who cares?". Maybe you could expand a little, or clarify, in order not to confuse the IP editor? --NorwegianBlue ^talk 06:34, 12 April 2012 (UTC)

Well, they are more or less the same thing. --Trovatore (talk) 09:22, 12 April 2012 (UTC)

Well-founded relation

Some 3 years ago, you had a long discussion on the above page, but somehow, it managed to miss an important point about infinite descending chains. I posted again, at the bottom of the talk page, on this. Perhaps you can clarify. linas (talk) 03:29, 21 April 2012 (UTC)

Never mind, brain is off. Time to go to bed. linas (talk) 03:40, 21 April 2012 (UTC)

I saw your recent edit

at a Warren Zevon album (I had made a similar correction elsewhere) and was wondering what you thought of the statement, "the novelty song "Werewolves of London"? Is W of L really a novelty song? Einar aka Carptrash (talk) 14:48, 15 May 2012 (UTC)

Seems borderline. I wouldn't have said so but I can see how someone might think otherwise. But then you could make the same claim about most of Zevon's opus, which seems reductive. --Trovatore (talk) 18:55, 15 May 2012 (UTC)

new comment on an archived question

Take a look: Wikipedia:Reference_desk/Archives/Computing/2012_May_19#Is_indexing_a_safety_risk.3F — Preceding unsigned comment added by OsmanRF34 (talk • contribs) 20:41, 23 May 2012 (UTC)

Misc

You may remember me from the AfD discussion,Crimes_involving_radioactive_substances.

Anyway, my dissertation advisor at Stevens just accepted a position at UNT, I think it may even be the Math Department, although his background is in Systems Engineering.

Small world...

Roodog2k (talk) 15:31, 25 May 2012 (UTC)

Category:Belgian inventions at WP:AN

Hello. This message is being sent to inform you that there is currently a discussion at Wikipedia:Administrators' noticeboard regarding an issue with which you may have been involved. The thread is "Category:Belgian inventions". Thank you. Andy Dingley (talk) 20:38, 12 June 2012 (UTC)

Vesalius

Hello. I can understand your viewpoint on "De_humani_corporis_fabrica" not being an actual invention as such. How could this be added / mentioned and be a better fit ? Maybe a category Belgian "Discoveries" or Belgian "contributions to sience" ? I also think "inventions" is someone specific as a word , but I would think it is currently used as a term to encompass innovation in general to avoid having too many categories at the bottom of pages. Also if you insist , I could make a subcategory "Flemish Inventions" . I will check this page again for an eventual reply . 3 days ago there was no category "Belgian Inventions" , together with a few others we are in the process of populating it . Vesalius is something we learn at school as being something that originated here , and that's why It was one of the items I thought should be mentioned . Regards 83.101.79.45 (talk) 06:52, 14 June 2012 (UTC)

Cardinal number - History section

You affirm that the history section of cardinal number article has [sources and citation]. But the whole section does not have any reference nor citation.

I have written a note, but another editor deletes it.

The whole section is awful and must be rewritten. I have written a warning on this, but also it was deleted. Citations and sources justifying correct statements must be added.

The section induces the following misunderstandings:

1) Cantor was the first to consider the one-to-one correspondence as a way of quantity, because previous authors are not cited.

2) Cantor first has formulated the one-to-one correspondence for finite sets and then has extended it for infinite ones.

3) Cantor has given a suitable notion of cardinal number

4) The current notion of cardinal number is essentially the Cantor concept.

Please read: http://en.wikipedia.org/wiki/Wikipedia:Administrators%27_noticeboard/Edit_warring#Edit_warring_in_Cardinal_number

Apologize the bad English

Regards

Carlos --Gonzalcg (talk) 21:48, 23 June 2012 (UTC)

Interlanguage wikipedia link within artile discussion

Some Chinese Wikipedian told me, English Wikipedia is a improper place to discuss this issue. I closed the discussion and moved to meta. Please continue the discussion in meta.--王小朋友 (talk) 08:17, 30 July 2012 (UTC)

RE: captain discussion

Hello. You have a new message about the page splitting discussion at Talk:Captain (United States)'s talk page. daintalk   01:03, 24 August 2012 (UTC)

Isaac B. Desha

Thanks for fixing my foul up in the lead. I wrote it carelessly. Acdixon ^{(talk · contribs)} 19:48, 27 August 2012 (UTC)

'Schematic'

	Wickid123:
	It may be personal, but ideas generally are... Even if that is an issue how then are new things created, and those ideas put forth? I really do think it deserves to be on a science-orientated-page. I doubt I am the first with the idea, but perhaps there is no evidence... So I don't know what to do. Thanks.Wickid123 (talk) 10:27, 12 September 2012 (UTC)

You need to find the ideas in what we call a "reliable source". That phrase does not necessarily have quite the meaning you would expect from normal English — see Wikipedia:Identifying reliable sources for more details. We're not allowed to just make stuff up here — even if it happens to be correct. --Trovatore (talk) 00:40, 12 September 2012 (UTC)

AC and Group Structure

Hi!

I have written a proposal for a new article. It's about the equivalence of AC and the existence of a group structure on every set. It's on my talk page. (It's about the only thing there, so you'll be able to locate it. Lead + two sections + references) I'd like to place it in the AC category if it's good enough, and perhaps link it from the AC article. Perhaps it should be in category Group too.

I think that the first section (Group Structure -> AC) is kind of neat. Well, perhaps not my presentation of it, but the main reasoning, which I think come from the second reference.

I'd be happy if you, Carl and JRSpriggs (and anybody else you feel ought to) could have a look at it. It's not in mint condition yet, but I don't want to spend too many more hours on it in case you all say booooooo. Keep in mind that I am just a layman.

Best Regards, Johan Nystrom YohanN7 (talk) 12:36, 15 September 2012 (UTC)

Back to the Incompleteness of Arithmetic

Hi, I assume you remember our discussion we had a week ago. I suspect there's still something left I couldn't understand from what you wrote: Is there a proposition - all of whose quantifiers range over natural numbers only, which is neither proved nor refuted in Second-order Arithmetic interpreted in Two-sorted First-order Logic?

Btw, what you wrote made me understand, that Second-order Arithmetic - interpreted in Second-order Logic - is not effective/computable, although it's complete, am I right? Additionally, you wrote "Second-order logic is extremely powerful (for example it either proves or refutes the continuum hypothesis, assuming, well, basically nothing)". What do you mean by "nothing"? Even not ZF?

77.127.133.106 (talk) 07:51, 20 September 2012 (UTC)

If you think you don't know the answer to my question, please say "I don't know", and I will ask at the reference desk. Thanks. 77.127.133.106 (talk) 21:11, 20 September 2012 (UTC)

No, I can answer it all. You know, these things are really not mysterious — with a few hints you should be able to figure them all out yourself.

First point: Yes, there is such a proposition. Take for example the proposition "ZFC is consistent". This can be expressed in the form you're asking for, for example

For every natural number n, n is not the Goedel number of a proof of 0=1 from the axioms of ZFC.

That proposition cannot be refuted by second-order arithmetic, because second-order arithmetic proves only true things, and the negation of the proposition is (presumably) false. On the other hand, neither can it be proved by second-order arithmetic, because the proposition implies that second-order arithmetic is consistent, which second-order arithmetic cannot prove.

Second paragraph — right. Full second-order arithmetic in second-order logic is complete, for the following reason. Given a model of the theory, for any genuine natural number n, it's easy to show that there is a corresponding object in the model, and moreover that this correspondence gives an isomorphic embedding from the genuine natural numbers into the natural numbers of the model. So all we need to know is that all natural numbers of the model can be obtained in this way.

But suppose not. Then let P be the predicate that picks out, from the natural numbers of the model, the ones that are obtained from the genuine natural numbers by the canonical embedding. Now apply the induction axiom to P.

And for the last point, right, you need much less than ZFC. Just enough to say that sets sort of behave like sets, and possibly the axiom of infinity; I'd have to think about it to see exactly what you need. --Trovatore (talk) 21:22, 20 September 2012 (UTC)

Thank you for your quick answer (like a missile). Since you didn't refer to the first half of my second point, namely: whether Second order Arithmetic - interpreted in Second-order Logic - is not effective/computable, so I guess it's really not. All the best. 77.127.133.106 (talk) 22:12, 20 September 2012 (UTC)

Right — if it were computable, you could violate the incompleteness theorem (just take every statement implied by the theory as an axiom). --Trovatore (talk) 23:17, 20 September 2012 (UTC)

Thanks. Btw, I understand that if Second order Arithmetic - minus Axiom of Induction - is added to Second-order Logic, then Axiom of Induction will be proved-or-refuted in the new system, am I right? If I am, then I understand that - the usual reason for adding Axiom of Induction to such a complete system - is generally just for the sake of convenience, i.e just in order to have more computable proofs for properties of natural numbers, correct? 77.127.133.106 (talk) 23:28, 20 September 2012 (UTC)

No, I don't think that's right. Induction is what "says" that we're talking about the natural numbers. Without induction, I don't see any reason the theory should be categorical. --Trovatore (talk) 23:30, 20 September 2012 (UTC)

Hence, Second-order Logic is powerful enough for proving-or-refuting the Hypothesis of Continuum, yet not powerful enough for proving-or-refuting Axiom of Induction. Correct? 77.127.133.106 (talk) 00:08, 21 September 2012 (UTC)

OK, so I overstated the case a slightly when I said SOL decides CH from "basically nothing". You need a little bit; enough, at least, to make sense of the question. For example the hereditarily finite sets are a structure for SOL, but it would be bizarre to ask whether CH is true or false in that structure.

But you don't need much. You need an infinite set, and you need the powerset of the powerset of that. You don't need separation, because separation is just true in the logic itself. You don't need choice, you don't need replacement. I'm not interested enough to pick through and decide whether you need union or pairing. Basically you just need enough to guarantee that the model has a referent for all the terms in the question. --Trovatore (talk) 07:35, 21 September 2012 (UTC)

Because you only need a finite number of axioms, in second-order logic with full semantics you can write a sentence which is satisfiable if and only if CH holds, in the signature that includes only equality. This is the sense in which full semantics decide the truth value of CH. But that sentence is neither provable nor disprovable in second-order logic, because if it was it would also be provable or disprovable in ZFC, but it is independent of ZFC. (The sentence simply says that if there exist addition and multiplication functions, and an order relation, that make the domain into an Archimedean ordered field, then every subset of the domain is either in bijection with the entire domain or is countable. No set-theoretic axioms are mentioned in the sentence, but the sentence can be interpreted as usual as a statement within ZFC about an arbitrary set which plays the role of the domain.)

Regarding "second-order arithmetic", some care is needed. First, "second-order arithmetic" is usually considered as a first order theory. But even if we study it in second-order semantics, it is generated from the same effective set of axioms as the first-order two-sorted version (we can include the choice axioms as well, depending on taste). The inference rules for second-order logic are no stronger than those for first-order logic. Thus nothing is provable that would not already be provable if we considered second-order arithmetic as a first-order theory. The effect of using full second-order semantics is simply to eliminate from consideration many models of the first order version (for example, models in which the sets don't range over all sets of individuals). Changing the semantics does not allow us to prove anything within the theory that was not already provable.

It's true that the theory of the standard model of arithmetic is a complete theory that is not effective, but this is true even in first-order logic. The effect of changing to full second-order semantics is that we eliminate all other models of second-order arithmetic from consideration. But if we just want to talk about the set of sentences true in the standard model we can do that even if we formalize arithmetic in first-order logic. — Carl (CBM · talk) 12:00, 21 September 2012 (UTC)

Well, now wait a minute, Carl — the rules of inference are much stronger in second-order logic. The rule of inference is that anything that is logically implied may be inferred, and because there's only one model (up to isomorphism), all true statements of arithmetic are logically implied, and therefore may be inferred. Of course the "rule" itself is not computable. --Trovatore (talk) 17:49, 21 September 2012 (UTC)

Yes, that "rule" is not computable, and it is not a rule of inference that anyone actually uses for second-order logic. In practice the rules that are used for second-order logic could also be used for first-order multi-sorted logic (and they are all verified by ZFC), with the result that there are many logical validities under full second order semantics that are not provable. The only difference between second-order logic as it is studied in the literature and first-order logic is in the semantics; the theories are syntactically interchangeable, including their deductive systems. — Carl (CBM · talk) 19:06, 21 September 2012 (UTC)

I don't know what you mean by "actually using" second-order logic. Anyway, for the benefit of our anonymous interlocutor, let me specify that by "provable" in second-order logic, what I mean is "logically implied" in second-order logic. I don't know what else anyone could mean. --Trovatore (talk) 19:22, 21 September 2012 (UTC)

A logic, after all, has a syntax and a semantics. Any reference on second-order logic is going to describe the deductive system that is normally used for it - e.g. section 3.2 of Shapiro's book. This consists of a usual deductive system for first-order logic in two sorts, something to correspond to the comprehension scheme, so that definable sets can be proven to exist, and often a system of principles analogous to the axiom of choice (Shapiro does include these, but Simpson does not, each having good reasons for their choice). In the literature, when someone talks about provability in second order logic they mean provability in a deductive system such as this. — Carl (CBM · talk) 19:51, 21 September 2012 (UTC)

Alright, fine. I don't want to mislead anyone through my possibly idiosyncratic use of terminology here. Restrahnt, please interpret my remarks as saying that second-order arithmetic as interpreted in second-order logic gives the complete theory in the sense of logical implication, rather than proof. And just a tiny bit of set theory, using second order logic, either logically implies or, what, "logically refutes" I guess? the continuum hypothesis. --Trovatore (talk) 20:09, 21 September 2012 (UTC)

You state that: "It's true that the theory of the standard model of arithmetic is a complete theory that is not effective, but this is true even in first-order logic". However, Trovatore has already presented a counter example, e.g. the proposition: "ZFC is consistent", or more formally: "For every natural number n, n is not the Goedel number of a proof of 0=1 from the axioms of ZFC". This proposition is neither provable nor disprovable in Second order Arithmetic (when considered as a first order theory), as Trovatore has already proved, hasn't he? 77.127.133.106 (talk) 14:42, 21 September 2012 (UTC)

The theory of the standard model of arithmetic (that is, true arithmetic but in the language of second-order arithmetic) has nothing at all to do with provability. In particular it does include the sentence Con(ZFC) because (1) the "numbers" in the standard model are the actual, standard natural numbers and (2) ZFC is consistent. — Carl (CBM · talk) 15:38, 21 September 2012 (UTC)

Monty Hall problem RFC

Hi! Over at Talk:Monty Hall problem#Conditional or Simple solutions for the Monty Hall problem? I assigned Abstain to your comments. If this is incorrect, please indicate "Proposal #1", "Proposal #2", or "Neither". Thanks! --Guy Macon (talk) 20:42, 20 September 2012 (UTC)

The infinite

Hi, I was intrigued by your post on the ref desk: "worst mistake...Aristotelian rejection of the completed infinite, in favor of the potential infinite." I've found this [1], but I'm not exactly sure how you're interpreting this sort of thing. Care to share your thoughts? SemanticMantis (talk) 00:41, 23 September 2012 (UTC)

The Unanswered Question

Greetings, Trovatore.

Always good to find someone who takes the detail of language seriously, even if we don't always agree on, er, the detail.

Which reminds me: You seem to have missed my question here. Or was your post some sort of humour that went over my head?

Cheers. -- Jack of Oz ^[Talk] 21:54, 8 October 2012 (UTC)

It was just a typo. I didn't see any point in belaboring it. --Trovatore (talk) 22:24, 8 October 2012 (UTC)

Fare enuf. -- Jack of Oz ^[Talk] 00:23, 9 October 2012 (UTC)

Other varieties of English

Re your comment on the spelling variations proposal at WP:VP/T, "just a few in some other varieties, usually barely distinguishable from British English, except for Canadian which is a mix", I had to laugh — I write some articles about Liberian topics, and it's downright tricky to write in Liberian English. Working here, I see tons of Liberian newspapers, and they seem basically to be a mix of US and British usage with tons of acronyms and occasional odd phrases (e.g. "I hold your foot" = "I beg you") thrown in. Nyttend (talk) 20:47, 6 November 2012 (UTC)

I don't think Liberian English is a recognized variety for ENGVAR purposes. The WP:TIES section applies only to English-speaking countries. --Trovatore (talk) 20:50, 6 November 2012 (UTC)

? Virtually everyone either speaks English or doesn't speak a Western language; English is the only official language, and it's dominant in business and print culture. Nyttend (talk) 21:01, 6 November 2012 (UTC)

Well, I'm not all that familiar with Liberia so I'll take your word for it. Still, let's face it, ENGVAR is mainly for keeping the peace between Yanks and Brits. The rest of it is mostly an afterthought, trying to make things look nice. --Trovatore (talk) 21:43, 6 November 2012 (UTC)

That's indisputable. I can't say that I've frequently seen situations when it was needed to prevent disputes between Jamaican English and Bangladeshi English, for example. Nyttend (talk) 21:52, 6 November 2012 (UTC)

I modified my comment after you made yours re "Third realm"

Since it was the opener for discussion, I modified my comment after you made yours re "Third realm", before others started commenting based on ambiguities in my opening comment. I am letting you know in case you might want to similarly modify yours before others start commenting. ParkSehJik (talk) 15:34, 26 November 2012 (UTC)

Cardinal numbers

Thanks for tidying up my edit on cardinal numbers. — Preceding unsigned comment added by Jason.grossman (talk • contribs) 01:43, 27 November 2012 (UTC)

I was wondering if this is legit

Please stop using talk pages such as Talk:Democracy for general discussion of the topic. They are for discussion related to improving the article; not for use as a forum or chat room. If you have specific questions about certain topics, consider visiting our reference desk and asking them there instead of on article talk pages. See here for more information. Thank you. Saddhiyama (talk) 10:27, 13 December 2012 (UTC)

Am I not allowed to write things that I think contribute to a specific page... (or is it that reference crap again, even though I linked something..)

I just felt it was so strange that it got deleted in a small talk, was wondering what you thought... or whoever It is on the democracy page (TALK) — Preceding unsigned comment added by Wickid123 (talk • contribs) 10:44, 13 December 2012 (UTC)

Absolutely abnormal number

In this edit you told another editor don't use Wikipedia to make up new jargon. If you look at the next two words after the phrase in question, you will see a reference Martin 2001 to a paper "Absolutely abnormal numbers" in the American Mathematical Monthly. Irrespective of the merits of the precise wording of the edit, it is clear that User:Nmondal was not making things up here. Deltahedron (talk) 21:08, 19 December 2012 (UTC)

OK, my bad; thanks for adding the cite. --Trovatore (talk) 21:13, 19 December 2012 (UTC)

Talkback

Hello, Trovatore. You have new messages at Talk:Auto Shankar.
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Paris1127 (talk) 22:46, 2 January 2013 (UTC)

Spacing in contractions, esp Italian

Hi Trovatore-- Re your watching Kwami's talkpage, I wonder if I might ask you another question, that I had posted at the Village Pump, but haven't yet received a response:

• It seems clear that you never space following the apostrophe where the contracted word is an article, such as with L'elisir d'amore, or in other situations where a word might be frequently contracted, such as, just for example, "Dov'è Angelotti?" or "Mario, consenti ch'io parli?". But then you sometimes get things that it's impossible to tell from the typography, but they look strange when they're not spaced, such as "Ho una casa nell' Honan" or "Nient' altro che denaro", "Quando me 'n vo soletta", "Sa dirmi, scusi, qual' è l'osteria?" etc. Are there rules for this?

In the meantime it looks as though I'm putting at least a few spaces in that latter series that ought not to be there. Milkunderwood (talk) 06:49, 8 February 2013 (UTC)

I also posted another question at Kwami's page, about "e shown in 'med', as opposed to 'mɛd'". He didn't know the answer, was just correcting the IPA. Fixed to 'ɛ'. Milkunderwood (talk) 06:59, 8 February 2013 (UTC)

Sorry, I don't think I can help you here. I don't know that I've ever used a space in this sort of situation. I have seen it, but not frequently enough to figure out any rules. --Trovatore (talk) 08:53, 8 February 2013 (UTC)

Well, I guess that does pretty much answer my question - that in general there should be no spacings at all. So that is a very helpful reply. Thank you. Milkunderwood (talk) 16:47, 8 February 2013 (UTC)

You shouldn't really take my word for detailed questions on Italian typography. --Trovatore (talk) 21:13, 8 February 2013 (UTC)

Talkback

Hello, Trovatore. You have new messages at Talk:Statement (logic).
Message added 22:39, 12 February 2013 (UTC). You can remove this notice at any time by removing the {{Talkback}} or {{Tb}} template.

Jason Quinn (talk) 22:39, 12 February 2013 (UTC)

Wikipedia:Reference_desk/Archives/Mathematics/2012_November_20#Guide_to_pronouncing_.28saying.29_mathematics_in_German

Hi, I was 96.46 in that conversation. Is what you wrote more than just a hunch on your part? It's hard to see why the French would render an English k by an sh sound, or what English really has anything to to do with things here.

But if they read Čech, which has that very diacritical mark, according to their own orthographic system but with allowance for the proper pronunciation of the first letter, the result would be precisely tchèche. 64.140.122.50 (talk) 05:05, 15 February 2013 (UTC)

Oh, I forgot that French would pronounce the che with a soft ch sound. I was thinking it would be a /k/. --Trovatore (talk) 05:14, 15 February 2013 (UTC)

All right. Thanks for clearing that up. 64.140.122.50 (talk) 06:03, 15 February 2013 (UTC)

Am I confused as to what Harvard citations are?

I was pointed to Special:WhatLinksHere/Template:Harvard citation for examples of articles using Harvard citations and I have yet to find an example there that uses parenthetical citations rather than footnotes. Am I incorrect that Harvard citations are parenthetical citations? Ryan Vesey 04:42, 18 February 2013 (UTC)

It appears that the template is used in some articles that don't have what I think of as Harvard cites. I'm a little confused on this point as well. One that does have parenthetical cites is Cauchy–Riemann equations. --Trovatore (talk) 04:47, 18 February 2013 (UTC)

Your revision today

I wish you had discussed this on the talk page first. Would you care to explain, on the talk page, what you mean here?:-

Undid revision 549743025 by Damorbel (talk) no, temperature is not kinetic energy. See Kittel & Kromer for the best accessible explanation of what temperature is.

--Damorbel (talk) 20:45, 11 April 2013 (UTC)

For one thing, the units of temperature and kinetic energy are not even the same.

Also a higher temperature not only makes particles move faster and thus have more kinetic energy, it also breaks bonds, change phases, and can create particle pairs (at sufficiently high temperatures). JRSpriggs (talk) 07:09, 12 April 2013 (UTC)

Thank You From a Necromancer

In January you gave me a really insightful and helpful response on the ref desk about Ehrenfeucht–Fraïssé games, my coming on here is fairly spotty and I didn't have a chance to reply when I first read it, so I ended up not without intending to. At any rate, though you've probably forgot what I'm even referring to at this point: Thank You:-) I love reading your contributions, a lot of your mathematical interests are the same as mine and you always seem to provide a breath of fresh insight.Phoenixia1177 (talk) 05:59, 19 April 2013 (UTC)

Thanks much! I had a lot of fun answering that question for its own sake, but it's nice to be appreciated too. --Trovatore (talk) 07:05, 19 April 2013 (UTC)

File:MixedFontBadness.png missing description details

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Talkback

Hello, Trovatore. You have new messages at ChrisGualtieri's talk page.
Message added 20:11, 10 May 2013 (UTC). You can remove this notice at any time by removing the {{Talkback}} or {{Tb}} template.

ChrisGualtieri (talk) 20:11, 10 May 2013 (UTC)

Redirects

Obviously, I disagree with all of the arguments for redirects, but as I am currently out numbered three to two, it is pointless to pursue the issue. Basically it is a non-issue anyway, like arguing over whether it is better to say this or that in a sentence. Both work and allow readers to get to the article in the link, and neither get there appreciably quicker. Apteva (talk) 03:33, 16 May 2013 (UTC)

Invitation to take a short survey about communication and efficiency of WikiProjects for my research

Hi Trovatore, I'm working on a project to study the running of WikiProject and possible performance measures for it. I learn from WikiProject Mathematics talk page that you are an active member of the project. I would like to invite you to take a short survey for my study. If you are available to take our survey, could you please reply an email to me? I'm new to Wikipedia, I can't send too many emails to other editors due to anti-spam measure. Thank you very much for your time. Xiangju (talk) 15:42, 22 May 2013 (UTC)

Misclick

Thanks for reverting me just now. It was, as you guessed, a misclick. I'll take the reference desk pages off my watchlist as I now realise that they are not for me. Warden (talk) 09:41, 12 June 2013 (UTC)

Neutron star, black holes on ref desk

You're right, he did answer my question, but i didnt realize.Rich (talk) 09:44, 23 June 2013 (UTC)

Its'

I mention it, and it magically appears. Weird, that. Medeis wasn't the user I was thinking of, but she still goes on to my List of Naughty Persons. -- Jack of Oz ^{[pleasantries]} 23:18, 5 August 2013 (UTC)

Individualism, recent edits.

Hi Trovatore, thanks for your helpful comments on this. My point was though that if you saw non-compliant changes, the duty should be on you to make the required changes, while respecting the good changes which were made by Hendrick 99, (and mine afterwards).

Just to delete both edits is a backward step. Why not change the words you think need changed (I don't speak American English!), and a gentle reminder to Hendrick 99 about his non-compliance? He wasn't just being non-compliant, in my view his edit contained some very worthwhile rephrasing independently of the language issues.

TonyClarke (talk) 19:08, 8 August 2013 (UTC)

Tony, if you examine the edit, the entire point of it was to change the English variety. This is especially clear if you examine other edits he made at about the same time. Any "good" changes that might have been included are beside the point — the entire edit should be reverted, and if you think he actually made any improvements (which is not clear to me), then those can be added separately. What good changes? --Trovatore (talk) 19:13, 8 August 2013 (UTC)

I would add that, by my lights, there is at least a small preference for stability in articles, so that edits need to justify themselves by actively improving the article. Any edit that neither helps nor harms an article, should be reverted; only edits that actually improve it deserve to stay. When a large number of changes are made in a single edit to widely varying parts of the article, if the edit has a controversial part, then the whole edit should be reverted and the changes discussed one-by-one. It is usually best to edit one piece at a time, so that it's clear what you're doing. --Trovatore (talk) 19:29, 8 August 2013 (UTC)

Hi Trovatore (a fellow biker I see!)

These are some of the changes from the beginning of the edit which I think improve the article in terms of simpler language and shorter words. The non-compliance is unfortunate, and a charitable approach would be that he/she used their own language, inadvertently non complying. Wonder if anyone has raised this with Hendrick 99?

I think there is clear evidence of an intention to improve the article, but no evidence in this edit at least of the intention to de-Americanise (or de-Americanize). Also I think we should be assessing edits on their own merits, not on the merits of previous work by the editor, unless that editor has been highlighted as persistently subversive or a vandal.

Your other point that edits should usually be made piecemeal: I don't think this should be a rule, as I have sometimes taken a whole article and rewritten it , then posted it, with no objections arising. Also I have sometimes revised a whole article or section for plain language, which can span the whole article and done piecemeal would be too burdensome. I think that is what Hendrick 99 was doing here.

So I think the article was improved, and the non-compliant parts are easily fixed. Since you raised the non-compliance, I feel you are best placed to sort it.

achieve precedence over -> supersede (simpler ) promote-> encourage (No noncompliance, also more accurate.) interests -> affairs (simpler, shorter word) makes the individual its focus -> centres around the individual (Less words, but non compliant so that not its main intent?) lend credence to -> favour, (shorter, non compliance but not its intent? would argue -> claims (shorter, better) precisely -> that it. (Shorter words)

I could go on!

In good faith

TonyClarke (talk) 11:24, 9 August 2013 (UTC)

I don't think you're looking at the whole picture of Hendrick 99's edits. It strains credulity to claim he/she was acting in good faith. Look at the diff I posted on talk:rights and how it breaks down — every change is either from an American spelling to a Commonwealth spelling, from a neutral word to a Commonwealth spelling, or from an American spelling to a neutral word. I broke them down one by one till I got tired of it, and there weren't any exceptions in the first five or six changes.

In this article he's been slightly cleverer, sticking in more irrelevant changes around them, but the agenda is still there. Here are some of the changes I think were the point of the edit:

• "emphasizes" -> "stresses" : Not particularly either better or worse as a word choice, but it takes out an "ize" spelling, which I think was why he did it.
• "makes the individual its focus" -> "centres around the individual": This one is absolutely a poorer word choice; the original is clearly better. There's no reason to do it except to get in the Commonwealth spelling of "centre"
• "the individualist does not lend credence to" -> "the individualist does not favour": Change in meaning here. Both the original and the new can be criticized. But the point is to add the "favour" spelling.
• "are based upon predominantly" -> "centre primarily around": Who says "centre around"? Again, that's a poorer word choice than the original.

So basically I think there's a clear agenda here and don't buy that he's acting in good faith. However, assuming arguendo that he were, there would still be enough questionable choices to revert. I agree with you that sometimes you can do a big noncontroversial cleanup edit, but then if anyone objects to any part of it, you should expect the whole thing to be reverted. You can't make a dozen different changes in the same edit and ask people to work from there, if they don't like parts of it — the whole thing gets reverted, and you discuss the changes from the status quo ante. --Trovatore (talk) 15:27, 9 August 2013 (UTC)

Not the way Jonesey95 saw one of the edits (see Hendrick 99 talk page, 4 August 2013 (UTC)), Jonesey was happy to change the bits which seemed wrong, while leaving what seemed good. Hendrick seems to me someone who is new and struggling on WIkipedia. To say this is a campaign to delete American wording is verging on paranoia: none of the other editors have seen his work this way.

To revert rather than amend is not helping someone who is struggling and perhaps a bit opinionated like most of us. It also doesn't help me, whose edit was caught up in your reversion. I don't think its fair that you are now expecting others, possibly me, to re insert the best bits of Hendrick 99's post, and also to reinsert the subsequent posts. But if you insist on maintaining your position, then so be it. Good luck. Happy cycling!

TonyClarke (talk) 17:45, 9 August 2013 (UTC)

advice

I've undone your comments to our newest troll, [2] restoring the hat you should not have opened. If you want to give personal advice he has a talk page. Please don't put it on the ref desk. μηδείς (talk) 02:22, 9 August 2013 (UTC)

Medeis, your hatting is frankly way out of line. I will undo it whenever I think it is appropriate. --Trovatore (talk) 02:28, 9 August 2013 (UTC)

You disappoint me. You are obviously a bit smarter than the average editor. I cannot see why you think giving a one-post troll personal advice, no reference, no link, on how he looks dancing is called for. μηδείς (talk) 02:46, 9 August 2013 (UTC)

Not a math journal

Hi, I started the following(*) in Talk:Saturated model. I have to agree with you about your note reverting me, "relevance is unclear". I'm used to a "saturated model" being one for which no more components can be added, given the limitations of the data. A saturated experimental design produces such a dataset, given a model form. A supersaturated experimental design produces a dataset insufficient to estimate all components of a given model, relegating the experimenter to a subset model of the original one. Is there a place here for that?

(*)WP can't be a math journal. There must be a common language introduction and explanation, with no special meanings for common words used. A more technical section with special meanings can follow, but without the others leading in before, it's not encyclopedic.

This is also my reason for putting the "Technical" template back into Type (model theory). Attleboro (talk) 17:57, 15 August 2013 (UTC)

Hi Attleboro,

You're right that WP is not a math journal. However it does not follow that all articles will be accessible to all readers, or will even have any part that is accessible to all readers. There is no upper limit at all to how difficult a topic can be, and still be appropriate for WP.

The appropriate criterion is, whether the material is as understandable as it reasonably can be, given the inherent difficulty of the subject matter.

I don't even necessarily disagree with you about the section you flagged in type (model theory). But you don't get to just plop the {{technical}} tag down there and leave, just because you personally don't get anything out of it. How do we know you have the background even to know whether it's written overly technically, given the subject matter? --Trovatore (talk) 18:34, 15 August 2013 (UTC)

Oh, as to the question about saturated models: There's a hatnote at the top of the saturated model article, directing you to the article on structural equation modeling, which may be what you're looking for. If that meaning is one that a lot of people are looking for, then it's possible that saturated model ought to be a disambig page. I'm not opposed to that if it's justified; please bring it up on the talk page. --Trovatore (talk) 18:37, 15 August 2013 (UTC)

Thanks for pointing out that note. I have a sneaking suspicion there may be a way to get from the formal definition in the article to the more common usage, or vice versa, but it's beyond me at the moment. I really disagree about no part of some articles being accessible to all readers. Otherwise, why separate WP by languages? Without a common language introductory section, the Tower of Babel looms over us all. Attleboro (talk) 20:20, 15 August 2013 (UTC)

If there's a connection between the model-theory usage and the statistics usage, it's completely obscure to me. But then I don't know anything about the stats usage, so I can't prove it either way. But if there is, I expect it's almost by coincidence; I don't think there are a lot of workers who do both model theory and statistics, so most likely the usages developed independently and in ignorance of each other.

We are using the same language, English. No one knows all of English, though. --Trovatore (talk) 20:43, 15 August 2013 (UTC)

Ice Hockey

My mistake. I saw that the IP editor was changing the English styles and assumed they were changing them from the established usage.--Asher196 (talk) 03:22, 30 August 2013 (UTC)

Easy mistake. --Trovatore (talk) 07:11, 30 August 2013 (UTC)

Godel

I don't see why there should be a top level religion section. Check out the other articles on people. Very few of them have religion sections at all and those that due have more filled out about other parts of the persons life. Should every article about a person have a religion section? Or is there something particularly important involving Kurt Gödel and religion that makes it worth mentioning? I don't think either is the case but maybe I am missing something. To me it is not more worthy of having its own section than say Godel's political views or something. Lonjers (talk) 02:35, 28 September 2013 (UTC)

Blah, I guess to be clear I am not disputing this based on a lack of information but based on notoriety/importance. Lonjers (talk) 02:40, 28 September 2013 (UTC)

Well, this is not something where there's going to be an absolute answer, but my feeling is that this material is more important for Goedel than it would be for a lot of other math/philosophy folks. Among latter-20th-century analytic philosophers, Goedel was one of the very few (at least, not coming from the perspective of a specific revealed-theological system) who openly challenged materialism and was willing to say he though the ego survives death. --Trovatore (talk) 20:10, 28 September 2013 (UTC)

Ron Paul

The piped link I supplied goes to a particular section of the article. This is because I did a WP:BLAR on the Peace & Prosperity article. Please let me know here what you think. – S. Rich (talk) 04:55, 30 September 2013 (UTC)

I fixed the redirect so that it goes to that section. If the Peace & Prosperity article is someday revived, the redirect will automatically go to the right place, but the pipe would not. --Trovatore (talk) 04:58, 30 September 2013 (UTC)

(edit conflict) Oh! I see what you've done on the redirect article. So is there a need to redo the other "what links here" articles? Thanks. – S. Rich (talk) 04:59, 30 September 2013 (UTC)

UPDATING AN AGED PICTURE

Hi Mike !

I was wondering if you can help me to update an aged picture for this guy "Salvatore Cuffaro". The picture currently on display is very old (2006) and the guy has also drastically changed in appearance becoming remarkably thinner. He was a former italian politician now jailed.

Here are 2 more recent images one is in b/w .. the other in colour .. as you can see the looks very different from the pic that is actually on display

http://www.sciclinews.com/immagini_articoli/1355416600_cuffaro_dimagrito.jpg

http://www.pellerito.it/wp-content/uploads/2013/10/cuffaro.jpg

Thanks very much for your help.

) — Preceding unsigned comment added by 88.112.193.20 (talk) 08:57, 25 October 2013 (UTC)

I don't even recognize the name, so I doubt I can really help. Good luck! --Trovatore (talk) 16:35, 25 October 2013 (UTC)

He is this one :

http://en.wikipedia.org/wiki/Salvatore_Cuffaro — Preceding unsigned comment added by 88.112.193.20 (talk) 00:29, 26 October 2013 (UTC)

Well, OK, I was being slightly euphemistic. I suppose I could help if I really wanted to — I could go digging around and see if anyone has a recent PD photo of him (unlikely but you never know). But why me, given that I never heard of him? Surely you're just as qualified to do it as I am (maybe more so, since you know something about hime to start with)? --Trovatore (talk) 00:43, 26 October 2013 (UTC)

Andy

Can you maybe comment on Andy's page. I generally find his hattings helpful, but this just seems overboard. I don't want to have to take this to uw3rr. μηδείς (talk) 04:36, 20 November 2013 (UTC)

Compact space

I agree with your edit; I wanted to link it as point-set topology (which was recently split from general topology), but I thought people wouldn't know what it is. Should I link to it anyways? General topology is no longer a helpful link for basics in topology, so I would liketo change it to something, but I would appreciate your feedback.Brirush (talk) 02:55, 30 November 2013 (UTC)

I think your new work at point-set topology looks good, but I would like to see it at general topology instead. I don't think the subjects are different enough for two articles. I've started a discussion at talk:general topology; comment invited there. --Trovatore (talk) 03:00, 30 November 2013 (UTC)

topoligical

I doubt "topoligical" exists in any English variant. Please be more careful before reverting, it is extremely annoying to have good faith edits reverted blindly. As to "neighbourhood" / "neighborhood" I have never before seen the "neighborhood" variant (I am Portuguese), and so I understand the correction, but it would be appreciate that a good faith edit would deserve more than blunt revert with some automated summary. - Nabla (talk) 00:47, 6 December 2013 (UTC)

I restored the good spelling correction. I deliberately did two edits, one as an undo to point out the ENGVAR issue (it wasn't just an automated summary; I explained), followed by a second one to restore your fix to "topoligical". --Trovatore (talk) 00:56, 6 December 2013 (UTC)

You reverted the good spelling correction. - Nabla (talk) 01:52, 6 December 2013 (UTC)

In the first edit. Then I immediately put it back. As I explained, this was on purpose. --Trovatore (talk) 02:10, 6 December 2013 (UTC)

You reverted a good faith edit, and a good edit, for no good reason, except imposing some English variant, on purpose. Exactly how does that help? - Nabla (talk) 10:45, 14 December 2013 (UTC)

He did not "revert" an edit- that would have led to an edit summary that begins with the word "Reverted". He undid an edit, and appropriately, because it was not appropriate to change "neighborhood" to "neighbourhood". It would also be inappropriate to change "neighbourhood" to "neighborhood" in an article that uses British spelling. Then he re-did the useful part of the edit to fix the spelling of "topological". I don't see any issue. — Carl (CBM · talk) 15:37, 14 December 2013 (UTC)

Removal of the trajectory section in Exponentiation

Trovatore, that is ridiculous. Have you indeed just removed the x^y curvature trajectory section there, which also contained reputable sources about such trajectories (and also a text, not only the illustrating pic!), because this section would teach in your opinion the topic not anymore tranquilly and gently enough?

All mathematical topics which are not content in any known teaching plans of schools should kept away from all encyclopedias?? --MathLine (talk) 23:46, 7 December 2013 (UTC)

We're not supposed to teach at all. Wikipedia is a reference work, not a textbook. The question is, is that section something that one would normally expect to find in a reference work on exponentiation in general?

My opinion is, it is not. But certainly the matter is open for discussion. Feel free to open a section on the talk page. --Trovatore (talk) 02:20, 8 December 2013 (UTC)

Confusing leads in field hockey articles.

2013 Men's Hockey Junior World Cup is an article with out field hockey being distinguished in the lead. To me its confusing, but i am unable to do anything. Can someone take a look at it. — Preceding unsigned comment added by 76.64.228.14 (talk) 00:58, 17 December 2013 (UTC)

I don't see a real problem here. The first link is to Hockey Junior World Cup, and the first link there is to field hockey, unpiped, so that the reader sees "field hockey" in the text. The 2013 Men's Hockey Junior World Cup article is in near-stub state; if it's expanded to talk about "hockey", as opposed to proper names that contain "hockey", then yes, it should say "field hockey" at first reference.

I'm not quite sure what you mean you're "unable to do anything" -- the article is not semi-protected; you can edit it if you want to. --Trovatore (talk) 07:21, 17 December 2013 (UTC)

Infinity

Hi Trovatore, while I generally support and respect your edits and opinions, I can not see how you could justify the statements about infinity that I removed and you reverted to. I'm sure that this has been discussed somewhere and you might point me to that, but I have spent too many years disabusing students of such notions to be easily convinced that I am wrong about this. I do not wish to be involved in any edit wars, but I do feel strongly about this, and would like to hear your rationale before I remove the offending remarks as being unsourced. Bill Cherowitzo (talk) 18:37, 19 December 2013 (UTC)

Sorry, I have a bit of a chip on my shoulder about the meaningless "infinity is not a number" assertion; neither "infinity" nor "number" is well enough specified to be able to recover any information from that cliché. There are certainly things called "infinity" in some contexts, that are also called "numbers" in some contexts. The language you removed seemed to me to be talking primarily about the infinity of the extended reals. --Trovatore (talk) 19:47, 19 December 2013 (UTC)

Interesting, but here are a couple of random thoughts. I don't see how the even more vague "...often treated as if it were a number" can have any more meaning than the cliché. While I have found the cliché to be pedagogically useful at times, I do agree that it is not well enough specified to be considered as a meta-theorem. When infinity is used in the context of the extended reals or any one-point compactification, it is the symbol and not the concept which is being used. If it takes on any numerical aspects, it is because it is defined to have them, they are not intrinsic. The only property that is implied by the use of this symbol, and the one that makes this a natural choice, is its lack of membership in the set being extended. Note that I am not arguing against the existence of infinite numerical things (hyperreals, infinite cardinals or ordinals, etc.). These things have numerical qualities because of their definitions, not because of their trans-finite nature. Also, the projective geometer's "points and lines at infinity" have no numerical connotation at all, so "often" would have to exclude geometric and topological uses. Not surprisingly, I find the sentence I removed as both inaccurate and misleading and I think we are doing a dis-service to the readers who come to this page looking for clarification of their own confused views of infinity. I'll put my thoughts on how I'd like to fix the article on its talk page. Bill Cherowitzo (talk) 18:52, 20 December 2013 (UTC)

Hmm, no, I don't really agree with your take on the extended reals. It's not just a symbol. It's an (extended) "number" bigger than any finite number. That's conceptually infinity. --Trovatore (talk) 19:23, 20 December 2013 (UTC)

Please indulge me for just a little longer. I am not trying to argue for my POV but rather attempting to clarify my thinking, and that is easier to do in dialogue (at least for me). In your response you talk about the (extended) "number", an infinite object, and I am perfectly ok with that (I'd prefer to call it a transfinite number, but that is just a minor point). Then you say that it is conceptually infinity and all sorts of red flags go up in my mind. It seems that I am reluctant to use the term "infinity" in reference to an object. Yet, when talking about elliptic curves, the point at infinity is routinely denoted by ∞ and is called "infinity" and I am perfectly happy with that! The two situations appear to be analogous so I am looking for an explanation (other than the possibility that I am schizophrenic ;^)) of why I see them differently. I think that in the elliptic curve case I can accept that usage because it is totally formalistic and symbolic–there is nothing intrinsically special about the point in question, its special role is an accident of the choice of coordinates. In order to make the extended reals work for me, without the red flags, I need to transfer this formalistic view to them, which is what I meant when I said that infinity was just being used as a symbol. So, does any of this make sense or am I creating a mountain out of a mole hill? Are there any implications here for how to organize the infinity article? Bill Cherowitzo (talk) 19:17, 21 December 2013 (UTC)

Before you start reorganizing the article Infinity, you should read the article Finite set and realize that infinite sets are the norm and finite sets are the special case. JRSpriggs (talk) 03:15, 22 December 2013 (UTC)

Hi Bill, OK, maybe this will clarify how I see things a bit.

I remember listening to a baseball announcer talking about a pitcher who had recently been called up to the majors. He had an earned run charged to him, but he had not yet gotten anybody out.

The announcer said, "The next time this guy gets an out, his ERA will go down (from what it is now). Because it is infinity."

Was he wrong? I don't think he was wrong. He was implicitly working in the structure [0,∞] (or, well, the corresponding thing on the rationals, if you want to get picky). The pitcher's ERA was something over 0, which was ∞. That was a worse ERA than it was possible to have if you had ever gotten anybody out, so it was correctly called ∞. To me this is not a formalistic trick; I'd call it the reality, correctly understood.

I don't know whether you buy this or not, but hopefully it makes it clearer how I'm looking at it. --Trovatore (talk) 21:00, 22 December 2013 (UTC)

Inaccessible cardinal

Hey, I saw your revert. Why not just correct the text. The letters should still be defined before they're used, not after. The bits of that article are out of order. Crasshopper (talk) 21:58, 19 January 2014 (UTC)

On reviewing the passage in question, I do kind of think you have a point. Unfortunately the text is in worse shape than I realized and it's not a trivial fix. I really just looked at the diff of your edit and thought it wasn't really in the right direction, which I still think, but I'm not sure what the best solution is. --Trovatore (talk) 06:46, 20 January 2014 (UTC)

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Borel σ-algebra

Continuing our discussion on that article ... Yeah, it didn't occur to me to use the axiom of choice, but I get your explanation. I'd like to hear more about the representation you mention (for my own curiosity). I'm guessing it depends on the axiom of choice too, as well as other high-level set theory. It would be a stretch even to say I'm a novice in modern set theory, but I do have some acquaintance with it. Maybe you can give me the gist in terms that are more analytic or topological? Daren Cline 01:48, 5 March 2014 (UTC) — Preceding unsigned comment added by Darencline (talk • contribs)

Alright, let's give it a shot. I think it's going to feel more like "computer programming" than analysis or topology, though.

Basically we're going to code up the ways that you can get a Borel set, into "trees". The trees we use in descriptive set theory generally "grow upside down", with the root at the top and the leaves at the bottom.

So the leaves are going to be the basic open sets — for the reals, for example, that might be open intervals, or open intervals with rational endpoints.

Now any open set is a union of countably many basic open sets. We can represent any open set by taking those basic open sets at the bottom, and putting a root node one level above them. (If there happen to be only finitely many basic open sets, that's fine, just repeat some of them to get a countably infinite collection; doesn't cost anything.)

              ROOT
          /    |    \
       /       |      \
     /         |        \
   /           |         \
 LEAF0       LEAF1     LEAF2  ...

Now, say you have a tree that represents a Borel set, and you want to represent the complement of the set. Do that by putting just one node above it:

             NEW ROOT (represents complement of B)
                |
                |
                |
              OLD ROOT (represents B)
        (branches out into subtree here)

Suppose you have trees representing Borel sets B0, B1, B2, etc. Then you get a tree representing the union of those countably many sets by repeating the first picture above, except in place of LEAF0, LEAF1, etc, you put the root nodes of the trees representing B0, B1, etc, and let their subtrees branch out below that.

Now we can say that any tree formed in such a manner is a Borel code, and the Borel set it represents is its interpretation.

Then you can prove fairly straightforwardly that the Borel sets are exactly the interpretations of Borel codes. Axiom of choice? You do need a tiny bit, but only about the same amount that you need to prove that, say, F_σ is closed under countable unions. (The key step is that you have to show that interpretations of Borel codes are closed under countable unions. To do that, given countably many sets that are interpretations of Borel codes, you just take their Borel codes and create a new one by putting a new root at the top of them. But where choice comes in is that each of the countably many sets you're starting with may have many different Borel codes, and you need to pick a particular one.)

I haven't talked about how to code up these trees as real numbers — that's a separate discussion and not as important.

Helpful for a start? --Trovatore (talk) 17:33, 5 March 2014 (UTC)

Yes, quite helpful. On the surface, at least, it seems that the Borel code is essentially following the line of the construction of the Borel σ-algebra that we've been discussing, by choosing the particular combinations sets that lead to the one we want. Except the transfinite part is unclear. Or is it that you have this countably described construction for a particular Borel set but cannot account for all Borel sets without applying transfinite induction?

Even still, the complexity involved is why the monotone class theorem and Dynkin's π-λ theorem are so important in probability and analysis. An arbitrary Borel set is not something you want to compute anything with or for. Which brings me to another question: are those theorems used much elsewhere? Are there good uses which have little direct application to probability? (I've just modified and extended the article on π-system which currently has only probability applications shown. Sorry if I've gone off topic here.) --Daren Cline (talk) 18:56, 5 March 2014 (UTC)

"The transfinite part is unclear." It's sort of hiding.

You see how to get Borel codes for a $\Sigma _{1}^{0}$ set by putting a node above countably many leaves, right? So that tree has a "height" of 1.

Then you can get a $\Pi _{1}^{0}$ (i.e. closed) set by putting a single node above that, to represent the complement. Height, 2.

Now you can get a $\Sigma _{2}^{0}$ (i.e. F_σ) by putting a node above countably many codes for $\Pi _{1}^{0}$ sets. Height, 3.

And so on.

OK, so now suppose you have a code $T_{1}$ for a $\Sigma _{1}^{0}$ set, a code $T_{2}$ for a $\Sigma _{2}^{0}$ set, and so on. The heights of those trees are 1, 3, 5, and so on.

Now you want the code for the union of those countably many sets. So you put a new node that branches out to the old roots of each of those trees.

What's the height of this new tree? Obviously it's bigger than any finite number. This tree has height ω

Now you can make a code for the complement of that set (a $\Pi _{\omega }^{0}$ set); it has height ω+1.

And so on. So you see how the transfinite induction arises, actually, very naturally, so much so that you didn't quite notice it. --Trovatore (talk) 08:51, 6 March 2014 (UTC)

Now, as to what the codes are used for — actually, they're not used all that terribly often. You can do proofs by induction on the complexity of the code, but then you can also do induction on the Borel rank (that's the least ordinal α such that the set is $\Sigma _{\alpha }^{0}$), so they're not really necessary for that. The reason I brought them up is that I think that they're a nice "concrete" illustration of how a Borel set is "constructed" from open sets. You don't have to think of the Borel sets as just this amorphous mass of sets that just arbitrarily have to be there if you have the opens and the closure properties — the code gives you a reason that a given set is Borel.

Other applications: Because you can code up a Borel code as a real number, you can prove that there are only as many Borel sets as there are real numbers.

But the only thing I know of that they're really indispensable for is when you have a function that, given a Borel set, gives you another Borel set (or some other object codable by a real), and you want to describe the complexity of that function. Then you might say that such a function is, for example, "continuous in the codes", meaning that there's a continuous function that, if you give it a Borel code for a set B, gives you a Borel code for f(B). --Trovatore (talk) 08:51, 6 March 2014 (UTC)

Got it. I don't know much about the theory of complexity but that's fascinating. Does it depend on the basis sets? That is, if you started with something other than open sets (like say, sets of the form (−∞, a] on the real line) then the complexity values are appropriately consistent? Are the continuous functions you mention likewise continuous in the basis sets as well?

But, actually, I was asking about uses of the monotone class theorem and Dynkin's π-λ theorem that are non-probabilistic; e.g., purely for set theory or topology or even mathematical philosophy. (Off topic, I know - but if you have ideas that are relatively simple to explain and might be included in articles like Dynkin's theorem and π-system, it would be great to see them.) --Daren Cline (talk) 14:50, 6 March 2014 (UTC)

I hope I'm not boring you. But something is still troubling me. In our discussion at σ-algebra you said

"The union of all the $\Sigma _{n}^{0}$ is called $\Sigma _{\omega }^{0}$, and it is not closed under complements."

But is "union" really the right word? Because to me that says, if $A\in \Sigma _{\omega }^{0}$ then $A\in \Sigma _{n}^{0}$ for some n, in which case $A^{c}\in \Sigma _{n+1}^{0}$ and thus $A^{c}\in \Sigma _{\omega }^{0}$. That's how I got confused before. --Daren Cline (talk) 14:16, 7 March 2014 (UTC)

Oh, sorry, my bad. $\Sigma _{\omega }^{0}$ is not the union of all the $\Sigma _{n}^{0}$. A set in $\Sigma _{\omega }^{0}$ is a union of countably many sets, each of which is from some $\Sigma _{n}^{0}$ (not necessarily the same n for each of the sets). --Trovatore (talk) 19:07, 7 March 2014 (UTC)

σ-algebra

Hi, Mike. Before I even get to the probability section I proposed on the Talk page for σ-algebra, I thought to look at the motivation section. While it is true that defining measure is the primary (and maybe the original) motivation for σ-algebras, it is only the beginning of their use. So the discussion currently there might seem a bit arcane to readers, and I don't think it fully answers some of the questions that have been posted about the article.

Anyway, to get to the point, I would like to expand the motivation section to consist of three subsections: the current discussion on measure, the definition of set limits to illustrate the necessity of countable unions and intersections, and an example about sub σ-algebras which also has countable aspects. To me, as a probabilist, the last point (using sub σ-algebras) is by far the most important, though of course measure is fundamental.

So here's my question: as a novice to this game, I'm not sure how best to present the idea of expanding that section, and specifically what it would look like. I have a version on my sandbox. I could just edit the page, but this will change the whole tone of the article and so maybe it's better to get some feedback first. I do think it's necessary to do something like this change, though. Daren Cline (talk) 03:43, 6 March 2014 (UTC)

Gisbert Hasenjaeger

Hello Trovatore. I understand you are a mathematician. I was wondering if you can possibly help me or perhaps you can point me in the correct direction. I looking to add a section into the Gisbert Hasenjaeger article which i've just created these past week, specifically related to his work, i.e his solution to Gödel's completeness theorem of 1929, which he published in the Journal of Symbolic Logic in 1953. I've had a look at the proof on JStor and Arxiv but can't understand it, not being a mathematician. There is a discussion of this translated page (from the German), [Life of Hasenjaeger] but understand this less. Any help would be appreciated. Thanks. scope_creep talk 00:16 21 March 2014 (UTC)

Sounds like fun! I'll see if I can take a look at it this weekend. --Trovatore (talk) 00:18, 21 March 2014 (UTC)

Your thoughtless edit

When you did this edit, did you read the next following sentence, "If it is discovered that two (or more) of these conditions hold, then all of them hold and ZFC+A1 is inconsistent and ZFC+A2 is inconsistent; in this case, these 'axioms' would no longer be considered large cardinal axioms."? You are supposing that this cannot happen, that is, that none of the "large cardinal axioms" will ever be found to be inconsistent, even though this has repeated happened in the past. JRSpriggs (talk) 04:57, 11 April 2014 (UTC)

I didn't see that sentence, no. But in any case the section is about an observation, not a theorem. In practice, none of the current large-cardinal axioms will ever be found to be inconsistent, because they are all actually true. --Trovatore (talk) 05:00, 11 April 2014 (UTC)

Definition of set

Hi Trovatore!

Would you mind commenting on this?. I posted it a while back and nobody has responded. I think Cantor's definition is perfect for the naive set theory article, but it isn't, in my opinion, a definition in axiomatic set theory. It's more like a recommendable way of thinking about sets. (Then again, perhaps I get it all wrong.) YohanN7 (talk) 21:35, 4 May 2014 (UTC)

You wrote

The classical antinomies derive from a error in the informal conceptualization (for example, conflating the intentional and extensional notions)

in the naïve set theory talk page. I'm not sure I understand what you mean, but I'd like to know precisely what you mean here. Can you give me a link to somewhere where the "intensional and extensional notions" we are taking about are defined/explained? YohanN7 (talk) 10:50, 7 May 2014 (UTC)

For example, I'd like to be able (on my own) to classify the phrase "There is a set of all sets" as an error/not an error in the informal conceptualization (of what exacly)? Is "conceptualization" a "stepping stone" towards "concretization"? Parts of my problems are linguistic, other parts are, I guess you could say, conceptual within our present context.

Reading Trovatore isn't always always entirely without pain (but sometimes worth it) :D YohanN7 (talk) 14:56, 7 May 2014 (UTC)

Still not clear what happened

I'm still not clear what happened with [this edit].

Since DisillusionedBitterAndKnackered has un-reverted the edit, are we now clear that an exception to a spelling difference does not have to be a spelling difference? It could be, if it was a different spelling difference, but it doesn't have to be one. His point was that, as a suffix derived from -ιζειν, burglarize shouldn't have been in the list, not that it wasn't an exception - he just was in too much rush to clarify that.

Graham.Fountain | Talk 17:50, 6 May 2014 (UTC)

An exception to a spelling difference doesn't have to be a spelling difference, but I still don't think it's appropriate for inclusion in the article about spelling differences. We just shouldn't mention it at all. That's my opinion. But it's a reasonably close call, and I don't care enough to press the point. --Trovatore (talk) 19:46, 6 May 2014 (UTC)

Well, if you are okay with agreeing to disagree, so am I.

It's just that I've never understood why you see this exception as fundamentally different from the others that are, also, not spelling differences between the US and UK, e.g. all those words in cis (to cut) and vis (to see). But that’s because - by the rule as you've given it - all these exceptions should go as well.

The only thing I can think of is that unlike these words, which are always correctly spelt/spelled with -ise, it's not an exception to the run of the mill "-ize words" in American English.

If that is the case, and common to other American English users, should it be even better underscored as an "exceptional exception", i.e. an exception to the -ize v. -ise spelling difference, but not actually an exceptional spelling in American English?

Graham.Fountain | Talk 10:47, 7 May 2014 (UTC)

Infinite book embeddings

Re this edit: I don't believe there is anything wrong in principle with the definition of books with arbitrarily large infinite cardinal numbers of pages. Such a book couldn't be embedded into Euclidean space any more, but that's a different question. However, I think all the actual publications about book embeddings concern finite graphs and finitely many pages. —David Eppstein (talk) 20:57, 20 June 2014 (UTC)

PS If one wanted to extend the definition to infinite graphs, a bigger limiting factor is the placement of the vertices on the spine. Do you require that they be placed on an actual Euclidean half-plane, with the edges drawn as actual curves? Or do you merely require that the vertices be given a total order, and the edges partitioned into subsets of edges called pages, such that no two edges in the same page have endpoints whose intervals overlap properly? For finite graphs it's all the same but for infinite graphs these give different definitions. I would prefer the more abstract total-order definition, because it doesn't restrict the cardinality of the vertices, but again I don't think anything has been published on this. —David Eppstein (talk) 21:08, 20 June 2014 (UTC)

Well, I was going by what it said in the article, which claims that the spine is a "line", which I took to mean a copy of R (or subinterval of R). --Trovatore (talk) 21:15, 20 June 2014 (UTC)

Norton's dome

Hi: you're absolutely right, g must be in the denominator in that equation for everything else in the rest of the paper to be independent of the value of g. I should have caught that, but didn't. Thanks for spotting it. -- The Anome (talk) 09:07, 6 August 2014 (UTC)

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Subset notation (ad nauseam)

Hi Trovatore, I find no fault with your recent edits at Subset and I realize that this notational difficulty has been discussed for a long time. I've read most of the discussion concerning conventions and have been puzzled by the fact that your perception of how commonly the different symbols are used differs from my own. In looking at the literature search, I was struck by two things. Firstly, some authors have used more than one convention (specifically, at least both Jech and Rotman have books in which they use ⊆) and secondly, I found the listing to be mostly missing the lower level texts. I think that this is important since students are usually first exposed to these notations primarily in these texts, and the readers of the subset page are not likely to have been exposed to higher level texts. I did a little survey of 14 texts in the "Introduction to Proofs" category and found that 8 used ⊆ for subset and ⊂ for proper subset and the other 6 use ⊆ for subset and had no special symbol for proper subset. In short, of the 14 texts at this level that I have on my bookshelf, none used ⊂ for subset. I have this number of such texts because I have been teaching this course for a long time, but these have not formed my perceptions. I distinctly recall being upset when I first read Halmos' Naive Set Theory because of his choice of subset notation (it jarred my sensibilities at that time) and that was about 40 years ago. I'm not exactly sure why I am telling you all of this, I'm not trying to convince you of anything, I just wanted to give you something to counterbalance your own perceptions. Bill Cherowitzo (talk) 20:32, 3 September 2014 (UTC)

You good with the title change proposed in the Lead discussion? Changing the history redirect?

Perhaps: Counting, Whole, and Natural Numbers -- see the discussion on the lead.

You good with the "history of numbers" redirect going instead to "History of mathematics or Number." as suggested by 50.53... (There is a conversation on in the "Translation ..." section.) ? Thomas Walker Lynch (talk) 07:36, 12 October 2014 (UTC)

Before making such proposals, it would be a good idea to read the policies for article titles and deletions and the guidelines for redirect deletion. --50.53.38.70 (talk) 08:13, 12 October 2014 (UTC)

I am traveling and do not have time to evaluate the proposal at the moment. I do appreciate the notice, but if someone would briefly summarize the proposal in a sentence or two for me, that would be much appreciated. --Trovatore (talk) 08:30, 12 October 2014 (UTC)

A proposal for changing the History of numbers redirect is at Talk:History of numbers. --50.53.49.222 (talk) 13:16, 12 October 2014 (UTC)

Logical quotation

Sometimes someone can feel that they are the only person supporting a position because no one else joins in on their side of a debate. As you should have been able to tell from my one comment in the section Wikipedia talk:Manual of Style#Logical quotation I hold a similar position on the issue, in fact you were doing such a good job at expressing my point of view I left you to it. -- PBS (talk) 11:09, 12 October 2014 (UTC)

Your edit to Word count

Undid revision 638857511 by Jhawkinson (talk) It *isn't* better than nothing

Why do you say that? Novella#Versus_novelette puts in context the distinction. Yes, it is on the Novella page rather than on a purpose Novelette page, but so what? Please explain. jhawkinson (talk) 02:44, 20 December 2014 (UTC)

Because novella is already linked in the table item just above! What's the point of linking it twice? There's nothing wrong with just not having a link there. --Trovatore (talk) 03:21, 20 December 2014 (UTC)

A link to Novella#Versus_novelette is nothing like a link to Novella. One is a deep link to relevant text, the other is a broad link to a complex article with multiple aspects. jhawkinson (talk) 03:36, 20 December 2014 (UTC)

OK, fair enough. I hate piped links in general, which probably biased me a bit. --Trovatore (talk) 04:36, 20 December 2014 (UTC)

Global account

Hi Trovatore! As a Steward I'm involved in the upcoming unification of all accounts organized by the Wikimedia Foundation (see m:Single User Login finalisation announcement). By looking at your account, I realized that you don't have a global account yet. In order to secure your name, I recommend you to create such account on your own by submitting your password on Special:MergeAccount and unifying your local accounts. If you have any problems with doing that or further questions, please don't hesitate to ping me with {{ping|DerHexer}}. Cheers, —DerHexer (Talk) 01:42, 3 January 2015 (UTC)

Natural numbers

You and D.Lazard have deleted a badly written section in the article Natural numbers. I did a detailed critique of the material on the talk page, and deleted it again. It's back. I'd appreciate it if you would take a look. Rick Norwood (talk) 16:41, 26 February 2015 (UTC)

Unsourced stubs

If you cannot find the time to locate a single third-party reliable source to demonstrate notability for a topic, please don't find the time to create an article at all.—Kww(talk) 14:11, 27 February 2015 (UTC)

I disagree. --Trovatore (talk) 18:54, 27 February 2015 (UTC)

Providing citations to external reliable sources is not some optional behaviour that you can can disagree about. It's mandated by WP:V. Don't create material unless you can provide inline citations to external reliable sources to support it.—Kww(talk) 23:18, 27 February 2015 (UTC)

See WP:DEADLINE. --Trovatore (talk) 23:21, 27 February 2015 (UTC)

Consider yourself warned: intentional violations of WP:V are grounds for blocking. You are not some young editor that doesn't know any better, you are an experienced editor that can be assumed to be completely aware of your responsibilities as an editor. You created a stub that made five unsourced assertions, at least two of which involve living persons (that the song was performed by Dion DiMucci and that the song was performed by the Animals). I have converted your article into a redirect until such time as someone provides inline citations supporting those assertions. If you restore the article without providing those citations, you will be blocked immediately. If I see that you continue to create articles with unsourced assertions, you will be blocked until you agree to stop.—Kww(talk) 01:56, 28 February 2015 (UTC)

Yes, that sounds like a good idea. Block every competent editor and don't let them back unless they do precisely as you tell them to in your all-mighty wisdom. (Not!) YohanN7 (talk) 13:25, 13 March 2015 (UTC)

Page move, new article

You changed Work Song to Work Song (Nat Adderly album). The musician's name was Nat Adderley, not Adderly. Could you change the title and the altered links, please? The same goes for Work Song (Nat Adderly song), which you created. (As Kww suggests, adding some sources to the new article would be good, too.) EddieHugh (talk) 17:12, 27 February 2015 (UTC)

Oh thanks, my bad. I'll go move those. I think there are some sources copyable from the article on the album, but beyond that, I was really just trying to get the organization of the articles right. Someone who's more of an expert can clean up the content. --Trovatore (talk) 18:51, 27 February 2015 (UTC)

Infinite Monkey Theorem

I noticed that you made a block revert of edits that I made to the above article. I have restored the changes I made in the Statistical Mechanics section but left the Lead for now. Would you please discuss on the Talk page thread I have started there before reverting my edits again. Thanks. DaveApter (talk) 12:49, 17 April 2015 (UTC)

Hillary Rodham Clinton - Move Discussion

Hi,

This is a notification to let you know that there is a requested move discussion ongoing at Talk:Hillary_Rodham_Clinton/April_2015_move_request#Requested_move. You are receiving this notification because you have previously participated in some capacity in naming discussions related to the article in question.

Thanks. And have a nice day. NickCT (talk) 18:55, 26 April 2015 (UTC)

The true model of set theory

Hi Trovatore, when people say "the true model" or "the standard model" of set theory, do they mean it in a platonic/realist sense? Like it really exists somewhere independent of our thought? I've been confused over this for years, to me in a formalist sense there can't be such thing as "the standard model of ZFC", because to a formalist a model is just a set in the meta theory (e.g. ZFC + there exist an inaccessible cardinal can be used to define models of ZFC in purely syntactic terms) in which we are studying ZFC. Why do people keep saying the standard/true of set theory? Am I misunderstanding something? — Preceding unsigned comment added by Money is tight (talk • contribs) 02:36, 17 June 2015 (UTC)

There is no bar, certainly, against a formalist talking about models the same way (s)he might talk about sets. For the formalist, presumably there aren't really any sets (or at least s/he isn't interested in their putative real existence), and similarly, there aren't really any models, but there is nothing that forbids using language that references them, while having a mental reservation that these are really just aids to thinking about formal sentences.

It's not a very satisfying view, to me, but it's coherent. And of course if there aren't any models, then there's also no true model. (But there are nevertheless formal ways of talking about the true model; not sure if that's what you're interested in and it's not what I'm focusing on in this response.)

What is really not coherent, in my view, is the attempt to have it both ways by claiming that (say) CH has an indeterminate truth value because it's true in some models in false in others. If what you really mean by that is simply that CH is neither formally provable nor formally refutable from (say) ZFC, then fine, say that; no one can really argue with that, given that it's been proven. And you can certainly explain that the notion of model is used in proving that.

But if you're trying to argue something more than just what happens with formal syntactic manipulations, an actual semantic indeterminate truth value, based on what happens in the models, well, then I have to call foul. At that point you're taking a realistic view of models, even if not of sets. And once you do that, you're in trouble, because we can make comparisons among the models, and we can talk about things that should or should not be true about the models, beyond just the first-order theories that they satisfy. So now it is no longer convincing if it ever was to say that the existence of models that disagree about CH mean that CH is indeterminate. --Trovatore (talk) 03:40, 17 June 2015 (UTC)

Ok that confirmed my thoughts. I've read a lot of your comments before and I believe you're a realist? I'm a formalist at heart so I have no problem in asserting CH has indeterminate truth value, however like any other mathematician I'm a bit of a realist and I think it's false. To realists, do you believe ZFC is a way for us finite beings to study the true model of set theory, and the axioms are suggested by our intuition of the von Neumann hierarchy? I.e. axiomatization is not of the primary importance, unlike to formalists it is. And can you explain a bit more about formal ways of talking about the true model? Money is tight (talk) 02:36, 18 June 2015 (UTC)

"Atomic" reverting

The first three comments are refactored out of edit summaries of WP:Manual of Style, which aren't for extended discussions.

Undid revision 667309593 by SMcCandlish (talk) *You* add back in the longstanding material. Not others' responsibility to figure out which is which. -- Trovatore 07:28, 17 June 2015‎

Complying with request, but you know as well as I do that when people are deleting material it is THEIR responsibility to delete the right parts. Longer passage has been there for years, shorter one from consensus discussion in June 2015. -- SMcCandlish 07:51, 17 June 2015

dummy edit: I completely disagree. That rule would allow editors to push stuff in by simply overwhelming the capacity of others to filter it. Reverts are cleanest when done atomically. -- Trovatore 07:54, 17 June 2015‎

Not applicable. I did not introduce enough material for that concern to arise. You're basing a "rule", or whatever you want to call it, of your own behavior on assumption of bad faith. I guess I can start a sandbox list of editors who prefer to have all of their work on a page mass-reverted, just to fix even a typo, and put you at the top of it, for future reference. Or is destructive, WP:POINTy reverting only okay when you do it to others? You did say you "completely disagree" with the idea of taking any responsibility to delete only the part in a series of edits that you actually object to. Just want to be clear on that. Or maybe you'd like to rephrase and (more to the point) rethink this anti-collaborative approach? Try "atomic" in the other sense, and edit like everyone else: Revert the smallest "particle" of change you can that addresses what your actual concern is, and leave as much of the new material as possible. That's how and why WP has millions of pages not ten. If you feel you have trouble articulating what your concerns are, please try the talk page, without reverting, until you can put your finger on what you think the issue is, and see if other people agree. Just a recommendation of course, but it seems to work for the majority of editors, so why not you? PS: I'm having trouble finding the "cleanliness of reverts" policy or guideline. Can you identify it for me? Can you explain what that even means to you?  — SMcCandlish ☺ ☏ ¢ ≽^ʌⱷ҅_ᴥⱷ^ʌ≼  10:52, 17 June 2015 (UTC)

PS: refactoring to User_talk; not MOS related.  — SMcCandlish ☺ ☏ ¢ ≽^ʌⱷ҅_ᴥⱷ^ʌ≼  00:35, 18 June 2015 (UTC)

If you revert me, yes, I prefer that you revert completely, rather than leaving a mess of different versions to sort out what's what. And I will continue to do the same, because it is the way that makes it easiest to follow everything that's going on. --Trovatore (talk) 02:53, 18 June 2015 (UTC)

Oh, just to fix a typo? No, I wouldn't do that, of course. I would just fix the typo. But that's for edits where I can understand the entire edit. You tend to leave many complicated edits all in a row. Moreover you do so on sensitive pages, where you are known to have strong views not everyone shares, and you do it without discussing first. I do not think this is collegial or even very transparent. --Trovatore (talk) 02:56, 18 June 2015 (UTC)

Messianic Judaism

I posted a comment on Messianic Judaism's talk page a few days back on the section you created concerning the dispute over whether it is syncretism or not. Please rejoin the discussion, so that it may rightly be called restorationism, and not syncretism, as is still currently implied. RuneMan3 (talk) 19:39, 4 September 2015 (UTC)

Justify your 'undo' action

This is ridiculous. A "whole number" can also be negative, while a "Natural number" is only positive (sometimes, even 0). Please justify your edit. VirtuOZ (talk) 12:49, 26 September 2015 (UTC)

It is very normal in English speaking countries for "whole number" and "natural number" to be synonyms, apart from the issue of whether 0 is included. In the ways the words are most commonly used, -1 is not a whole number, even though it is an integer. But, in any case, if you would like to change the redirect target, I recommend discussing it on Talk:Natural number. The redirect target has been stable for some time, and the target was discussed in detail before on the talk page, so although you might have suspected the change would be uncontroversial, actually it isn't. That makes it reasonable to undo the change unless there is visible consensus for it. — Carl (CBM · talk) 14:12, 26 September 2015 (UTC)

Well formulated; Accepted. I.e. 'Wikipedia-accepted' not mathematically-accepted, of course. It might even be my mistake for not checking if a talk page or version history exist (I'm not used to it, when it comes to reference pages), but I come from the world of math, and instantaneously that error was screaming to the sky and I had to take action. Good job and good day. VirtuOZ (talk) 16:16, 26 September 2015 (UTC)

One thing that always amazes me when editing here is how much variation there is in basic terminology. The definition of a "function" turns out to be a minefield! But if you look at any advanced topic, like cobordism or the Riemann hypothesis, there is usually no ambiguiity at all. A big part of this is that texts for non-advanced audiences tend to simplify things in different ways, of course, but everyone remembers the way that he or she was first taught a subject. — Carl (CBM · talk) 16:23, 26 September 2015 (UTC)

I did justify it. In the edit summary, I said "see previous discussion". There's not that much of it, not too much for you to read, but more than I want to recap. Do that first. Then we can talk. --Trovatore (talk) 17:56, 26 September 2015 (UTC)

Actually, there is a lot to read there, but as you can see from my previous comment here, I'm already 'technically' content. I still think the best solution was to keep that page as a disambiguation page, and don't understand why is it so necessary to turn it into a redirect page. VirtuOZ (talk) 23:11, 26 September 2015 (UTC)

A disambig would be OK with me if it would stay a pure disambig page. People kept trying to add actual content to it, which was inappropriate and disruptive.

Just by the way, in my experience, the term "whole number" is essentially unused in "the world of math", as you put it, so I'm still not sure what "error" you're talking about. I am familiar from it mostly from primary and secondary mathematics classes in the United States, which typically use the older and less useful sense of "natural number", the one that excludes zero. So then they need a term for the more natural and more useful notion, the one that includes zero, and they go with "whole number". But the term "whole number" is virtually never used in research mathematics. --Trovatore (talk) 01:30, 27 September 2015 (UTC)

Quantum Fields Fluctuation, Time Stop

On reading the second criterion for patent nonsense, I think it does apply, in that no one can copy-edit the article because it is incomprehensible. If anyone wants to speedy the article, that is fine with me. Robert McClenon (talk) 17:26, 28 September 2015 (UTC)

ArbCom elections are now open!

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You appear to be eligible to vote in the current Arbitration Committee election. The Arbitration Committee is the panel of editors responsible for conducting the Wikipedia arbitration process. It has the authority to enact binding solutions for disputes between editors, primarily related to serious behavioural issues that the community has been unable to resolve. This includes the ability to impose site bans, topic bans, editing restrictions, and other measures needed to maintain our editing environment. The arbitration policy describes the Committee's roles and responsibilities in greater detail. If you wish to participate, you are welcome to review the candidates' statements and submit your choices on the voting page. For the Election committee, MediaWiki message delivery (talk) 13:07, 23 November 2015 (UTC)

I reallly, really, really, really, really

...don't want to discuss this further at the ref desk, but isn't your "at least a mile further" comment the same as saying that wherever you are on the earth, there is always some other place at least a mile further away? If so, you are talking about a finte but unbounded universe. It's like a circular hallway. They hallway is finite, but you can keep trevelling along it as far as you like. μηδείς (talk) 23:17, 4 December 2015 (UTC)

Ah, just the example I was going to bring up, if this came up again.

You actually can't always get one mile farther away, on the surface of the Earth.

For simplicity, let's take the Earth to be a perfect sphere. It isn't, of course, but that fact complicates the discussion unnecessarily, without adding any conceptual clarity.

Then the farthest place from where you are is the antipodal point. From there, yes, you can go another mile in the same direction, but you don't get farther away. You actually get closer.

This is the exact distinction between a (spatially) finite and infinite universe. If the universe is finite, then there is some point p such that no point q is a mile farther from you than p is. There's a point a mile further along the same geodesic, but it isn't farther from you. It's actually closer. Just in a different direction.

On the other hand, if the universe is infinite, then no matter how far p is from you, there's another point q that's a mile farther from you. Not a mile further in the same direction. A mile farther, period.

I hope this clarifies the distinction I'm making? --Trovatore (talk) 00:29, 5 December 2015 (UTC)

Cute. No, I won't argue metaphysics. But in my Delaware Vally dialect further is the standard comparative form of far. "Farther" is abstruse. μηδείς (talk) 01:40, 5 December 2015 (UTC)

We don't need to argue metaphysics; I'd just like to get confirmation that the definition is clear. --Trovatore (talk) 01:51, 5 December 2015 (UTC)

@Medeis: For what it's worth I actually do follow a distinction along the lines of that described at [3]. Suppose Adolph and Bernie lead two groups of hikers to a hillside overlook near the horizon. Two hours later I see Bernie's group setting up camp on top the hill. As dusk settles in I see Adolph's group still going around in circles among some logging roads in the foreground halfway between me and the hilltop overlook. Now Bernie's group went farther but Adolf's group went further, and however incorrectly, I tend to draw a connection with Fuehrer. Wnt (talk) 18:12, 20 August 2016 (UTC)

Hello

I'm sorry for changing your comment. I thought - the reason for which you'd used the beginning of my previous username in your comment - was because it was my username when you wrote your comment, so I thought you didn't mind if I "adapted" your comment to the global change I'd made in my username. However, now I see you did mind, so I really apologize.

Anyways, please notice that the reason for which I changed my username, was because - when I saw the beginning of my previous username in your comment - I realized this username could be offensive. So, would you mind to change this username in your comment? Yours truly, HOTmag (talk) 08:27, 28 December 2015 (UTC)

OK, done. I don't know what you see as offensive, though. I've never understood what your username means, but the word "hoot" is not problematic in most contexts. --Trovatore (talk) 19:05, 28 December 2015 (UTC)

Thanks! Yes, the word "hoot" is usually not problematic. Generally, I don't give a hoot when I hear somebody hoot. Unless I hear the hoots of the audience in the football stadium, and feel like going back home. HOTmag (talk) 21:24, 28 December 2015 (UTC)

5-dimensional space

Appreciate your thoughts on the 5-dimensional space article, though I am uncomfortable with the lead that you restored as it somewhat misrepresents the concept. Although you were concerned that the former lead was too physics oriented, this is a physics article. I think we need to work on coming up with a better sentence that is more accurate but still understandable. I enjoy sandwiches (talk) 01:21, 10 January 2016 (UTC)

I completely disagree that it's a physics article. I see it as a math article first and foremost, with physics as a sidelight.

Why don't you explain your specific objections on the article talk page? --Trovatore (talk) 02:02, 10 January 2016 (UTC)

Interesting. Let me try and come up with a better sentence in the future when I have a bit more time, as I still think the lead sentence is incomplete. I will be conscientious of not making it overly convoluted, though welcome your thoughts. Will continue further discussion on the article's talk page if needed. I enjoy sandwiches (talk) 13:50, 13 January 2016 (UTC)

Good answer at RD/Math

		The Reference Desk Barnstar
		I've noticed you around for quite a while, but I especially wanted to compliment you for this empathetic reply. — Sebastian 18:45, 13 January 2016 (UTC)

Thanks! --Trovatore (talk) 23:19, 13 January 2016 (UTC)

Apologies

Hello. I'm sorry about that indent thing from a few months back. I was rude to you. Peter238 (talk) 00:44, 29 January 2016 (UTC)

Don't worry about it. --Trovatore (talk) 01:15, 29 January 2016 (UTC)

Sentence of the week award

"OK, first of all, let me come out of the closet here — yes, I am a dualist." :) SemanticMantis (talk) 17:49, 17 February 2016 (UTC)

Have A Cookie

For helping me educate myself

.

@Trovatore: when you undid my work on Magic (paranormal), I got all ready to fire off an indignant "WTF?", because your summary didn't really explain your rationale. In an unusual moment of self-reflection, I stopped and did a little research. Lo, and behold! I found that you were right to do so, and that all that slogging was unnecessary. *sigh*

So thanks for moving me to learn something.

Best regards,

*Septegram*Talk*Contributions* 22:29, 17 February 2016 (UTC)

Hi!

So, is the article talking about specific function symbols that have a determinate arity by convention? My doubt is, how can a symbol have arity before being interpreted? Thanks! --ExperiencedArticleFixer (talk) 00:22, 25 February 2016 (UTC)

The language includes arities for all the function symbols. The same symbol might have different arities, but only in different languages. --Trovatore (talk) 00:23, 25 February 2016 (UTC)

Oh, so within one and the same language you have a specific symbol that is intended to be unary, another different symbol which is intended to be binary, and so on? --ExperiencedArticleFixer (talk) 01:57, 25 February 2016 (UTC)

Right. Well, of course you don't have to have exactly one of each, but I don't suppose that's what you meant. --Trovatore (talk) 02:10, 25 February 2016 (UTC)

Thanks for sharing! Last questions: Are there standard symbols for each arity? Where can I find a list? --ExperiencedArticleFixer (talk) 13:43, 25 February 2016 (UTC)

No. JRSpriggs (talk) 00:11, 26 February 2016 (UTC)

"Reasonable"

SV's mass-RV action was not reasonable, as the edit summaries made clear what the different edits were for, requiring no work on anyone's part to just revert the bold changes, a discrete group that were not commingled with gnoming edits. This has been a long-term behavioral dispute with SV; I have objected to her "clobber every single thing the editor has done any time recently just to make a punitive point" actions for around ten years now. It is a civility and destructiveness behavioral problem. Please do not encourage it.  — SMcCandlish ☺ ☏ ¢ ≽^ʌⱷ҅_ᴥⱷ^ʌ≼  21:40, 23 March 2016 (UTC)

Stanton, you're looking at it wrong. The advantage of an atomic revert is that it minimizes the number of distinct versions. That simplifies matters for anyone looking at the history and trying to figure out what happens. It's not a punishment; it's just a procedural "best practice". --Trovatore (talk) 03:39, 25 March 2016 (UTC)

New quote in incompleteness theorem article

Hi Trovatore - I replaced the old "paraphrased" statement with a new quote from Panu Raatikainen's article in the SEP. This resolves a longstanding cn tag. I looked quite a bit for a direct quote that would have all the content of the previous paraphrase, but nobody seems to say things exactly that way. However, Raatikainen also had a useful quote about the truth of the Goedel sentence, which I inserted at the same time. I think the change is an improvement overall, even though the statement is not quite the same. The goal is not to downplay any aspect of the theorem, but to try to find a direct quote that can be used for the paraphrase, for the usual reasons. — Carl (CBM · talk) 14:56, 3 April 2016 (UTC)

At a quick scan, looks good. Thanks, Carl. --Trovatore (talk) 20:27, 3 April 2016 (UTC)

Why

EmpCarnivore (talk) 03:48, 16 April 2016 (UTC)Why did you remove my zero division post on talk

Because it wasn't related in any actionable way to improving the article. --Trovatore (talk) 04:35, 16 April 2016 (UTC)

Impostor

That wasn't me. That was an impostor User:Linguist1111, who was forging my signature. Linguist 111^talk 23:26, 22 April 2016 (UTC)

Pruned tree listed at Redirects for discussion

An editor has asked for a discussion to address the redirect Pruned tree. Since you had some involvement with the Pruned tree redirect, you might want to participate in the redirect discussion if you have not already done so. Stefan2 (talk) 16:21, 27 May 2016 (UTC)

Ordinal arithmetic

Hi Mike,

I'm writing a game that is based on ordinal numbers, but since I am not an expert on the topic I need some support. Is it ok if I occasionally ask you some questions to help my understanding?

First question - can you confirm that $2^{\omega \cdot 2}=\left(2^{\omega }\right)^{2}=\omega ^{2}$?

This seems straightforward to me, the reason I'm asking is that I've found an excellent ordinal calculator (http://www.mtnmath.com/ord/, http://www.mtnmath.com/ord/ordinal.pdf), which seems to give the wrong result for this. It says that $2^{\omega \cdot 2}$ is $\omega \cdot 2$, which makes no sense to me. Similarly, the accompanying paper says (in table 24) that $4^{w^{7}+3}=w^{7}\cdot 64$, where I expect $w^{w^{6}}\cdot 64$.

I wrote an email to the author with the bug report, including 4 different proofs that the calculator's result is wrong. He wrote back (which is a start) but simply dismissed me as some random guy that doesn't get ordinal arithmetic, without writing anything of substance or addressing my claims - which is exactly what I tried to avoid by explaining my case at length.

So I'd appreciate your confirmation that I'm not imagining things here.

Thanks, -- Meni Rosenfeld (talk) 09:54, 1 August 2016 (UTC)

To Meni Rosenfeld: Your calculations are correct and his are wrong. See Ordinal arithmetic. JRSpriggs (talk) 14:01, 1 August 2016 (UTC)

Thanks! Maybe I should leave Mike alone and bug you with my questions instead :)

Our article on the subject was indeed one of my sources in making sense of this.

I have a hard time wrapping my head around how someone like Paul (the author) could have spent so much time working on the ordinal calculator software and related papers, and have such a fundamental misunderstanding. It was bad enough when I thought it was just a bug that slipped into the software, but his response to me indicates he's truly confused about this. Do you have prior familiarity with his work? Is he known in the field?

This is a shame, among other things I'm writing my own implementation for ordinal arithmetic and I was hoping to use his works as a reference to verify correctness. But if they're erroneous about that who knows what other things they're wrong about. -- Meni Rosenfeld (talk) 17:31, 1 August 2016 (UTC)

Update: He has now acknowledged the problem. -- Meni Rosenfeld (talk) 06:25, 2 August 2016 (UTC)

Personally, I would like to see a calculator that can handle the Veblen function. JRSpriggs (talk) 01:27, 3 August 2016 (UTC)

There is support for the Veblen function in the calculator. What it can do with it exactly, compared with what could be done, I don't know. You should try it out I guess. -- Meni Rosenfeld (talk) 07:37, 3 August 2016 (UTC)

Help With Formatting

With this entry, how should I cite my change?

A simple link to Digital_root, or should I link to an outside source?

I am new to Wikipedia formatting and would appreciate any feedback. — Preceding unsigned comment added by Kd7tck (talk • contribs) 08:04, 20 August 2016 (UTC)

Hmm, the first question is to figure out whether it's worth mentioning, and if so, where in the article. I wouldn't be opposed to adding it as a consequence of the second-to-last "minor result", the one about perfect numbers other than 6 all ending in 1 base 9, which is the same thing as your observation. Technically some might argue that we need a reference even for this immediate corollary, but that would be awfully picky.

@Kd7tck:So you could do something like this, as an edit to that result:

• Every even perfect number ends in 6 or 28, base ten; and, with the only exception of 6, ends in 1, base 9.. Therefore in particular the digital root of every even perfect number other than 6 is 1.

How does that sound? --Trovatore (talk) 21:44, 20 August 2016 (UTC)

Thanks for the compliment

(provided you weren't being sarcastic, that is) I didn't even take the chance of cuing Vfrickey in on some of my 'First and Second Amendment' efforts here like sutari. :) Wnt (talk) 18:19, 20 August 2016 (UTC)

Totally sincere. I thought you expressed it beautifully. You should comment on the "hate speech" thread on one of the other refdesks. --Trovatore (talk) 21:36, 20 August 2016 (UTC)

Per your encouragement I kind of ranted on there, but the beauty may not be there. Wnt (talk) 01:59, 21 August 2016 (UTC)

Infinity

Re [4], thanks -- I didn't read carefully enough and had the misperception that the sentence I removed was a nonsequitur, when in fact it is connected naturally to the following part of the paragraph. (Actually I am somewhat skeptical that the paragraph on cosmology is a really sensible place to have that discussion, but whatever.) --JBL (talk) 16:05, 29 August 2016 (UTC)

You are invited to a discussion at MOS talkpage.

Hi, Trovatore,

I merged part of WP:BANDNAME into MOS:THECAPS in an attempt to make things less confusing, only to have it rudely undone without any explanation by Prickzi, I have asked him or her to please, then, discuss the reversion on the talk page, which he/she has so far refused to do. Will you please enter your opinion on if we should leave the merger in place or why not to have it in place, here: [5]? Nancy Pantzy (talk) 01:18, 20 September 2016 (UTC)

vocative O

Vocative O is capitalized, you say in your edit to Bach's cantata, but it isn't in the source, --Gerda Arendt (talk) 07:15, 19 October 2016 (UTC)

Hmm, this is a pretty standard rule of English. Whose translation is it in the first place? Any idea why it isn't instead the more literal come, thou sweet hour of death?

It seems to be the general sense at the MoS that we're allowed to (and should) correct minor stylistic idiosyncracies from sources. I don't necessarily agree with that as far as it's been taken, particularly when there is a systematic reason followed by experts in the field to do something different (the famous "bird" controversy), but my feeling would be that we probably should do so here. Not capitalizing "O" is about as strange as not capitalizing "I" — they're often treated in the same section of grammars; the two one-letter words that are always capitalized. --Trovatore (talk) 07:30, 19 October 2016 (UTC)

ArbCom Elections 2016: Voting now open!

Hello, Trovatore. Voting in the 2016 Arbitration Committee elections is open from Monday, 00:00, 21 November through Sunday, 23:59, 4 December to all unblocked users who have registered an account before Wednesday, 00:00, 28 October 2016 and have made at least 150 mainspace edits before Sunday, 00:00, 1 November 2016.

The Arbitration Committee is the panel of editors responsible for conducting the Wikipedia arbitration process. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose site bans, topic bans, editing restrictions, and other measures needed to maintain our editing environment. The arbitration policy describes the Committee's roles and responsibilities in greater detail.

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Need help with article on the Four dimensional shape, the Cubinder.

Hello fellow Wikipedian. I am in the process of creating an article about the 4D shape, the “cubinder”. It was previously red linked on other articles, and I was surprised to see it was not already an item listed for creation by Wiki Projects Mathematics, as the duocylinder and spheriender are already articles. I require help to improve the draft, as I require more formulae, sources, and additional information to create this article. You can access this page at User:Darnburn98/Cubinder, please come on over and help improve this article to get into the main space! Darnburn98 (talk) 23:34, 20 January 2017 (UTC)

If you want to be extremely technical about it...

...according to international law, the United States didn't actually declare war on Japan until official notice was delivered by the Secretary of State to the Japanese Embassy in Washington DC, or by the American Ambassador in Tokyo to the proper authorities there. The phrasing "Country declares war on country" is absolutely standard usage, and does not require specification of the mechanism behind it. And, yes, the President was formally involved, as the declaration was passed by Congress at his request. Congress could have passed a declaration on war without the President requesting it, but that's not how it happened. Beyond My Ken (talk) 20:45, 13 March 2017 (UTC)

As I said on the article talk page, you are trying to force too much interpretation into this stylistic choice. If you want to explain the extent of Hitler's personal authority, you should do it explicitly, where it can be discussed, and evidence and citations given. --Trovatore (talk) 20:56, 13 March 2017 (UTC)

Nope, I am trying to prevent a purely stylistic choice from distorting historical fact. Beyond My Ken (talk) 21:06, 13 March 2017 (UTC)

What distortion? Are you claiming that Germany did not declare war? --Trovatore (talk) 21:07, 13 March 2017 (UTC)

Please don't be disingenuous. I assume you've read my response to you on the talk page, and I give you credit as being more than intelligent enough to understand my point. Using parallel construction implies that they were parallel situations, when they most assuredly were not, for the many reason I've outlined before and won't repeat here. Rhetoric doesn't exists for its own sake, it's meant to exist in service to the information being transmitted. Beyond My Ken (talk) 21:20, 13 March 2017 (UTC)

I understand your point. But the problem is that you're coloring "the information being transmitted" without it being clear to the reader what you mean or where to find the sources. It would be better to make the point in explicit text.

Look, I'm an individualist; I don't believe in "Germany" (or "the United States" for that matter) as volitional entities. So I don't personally care about attributing the responsibility to "Germany", whatever that is. But if you're going to use language that removes the responsibility from "Germany" but assigns it to "the United States", then it needs to be explained explicitly, with citations. --Trovatore (talk) 21:28, 13 March 2017 (UTC)

Proposed deletion of File:QuoteMarks.jpg

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Last Temptation and whitewashing

I just want to say I very much agree with your position on Scorcese's Last Temptation and "white Washing." Firsly I see scores and scores of films set in the near East at that time that do not have that "see also." Secondly the genetic history of the Levant is complex, highly varied and the current genetic scholarship shows had more of the general Indo-European stock as it had not seen the major movements of people in from the Arabian Peninsula. There were many indo European groups there, in and for that matter in Mesopotamia and of course Anatolia as well at that time. Moreover there was a large influx and movement of people during the Macedonian and Hellenistic period which was in the fourth and third centuries BCE and in the Roman period as well. There is a absolutely no way to exclude the possibility that Jesus, if he existed, would not have looked like Dafoe, and there is the definite fact that more people there did look like that than today. The problem is how to counter this absurd absolutely position that no one in the levant could have looked like Dafoe, without getting tagged as saying or intending something else. I will go to that page and support your position. 76.100.252.109 (talk) 03:01, 13 May 2017 (UTC)

Um — I think you may have missed my point a little bit. I wasn't arguing that Jesus might have been white. I was arguing that casting a non-white historical figure with a white actor does not necessarily justify a see-also to whitewashing. --Trovatore (talk) 04:04, 13 May 2017 (UTC)

On television, I once saw the opera Die Walküre with Siegmund played by a white man and Sieglinde played by a black woman. Yet AFAIK, no one said that that was black-washing. JRSpriggs (talk) 07:28, 13 May 2017 (UTC)

Some people think it's a terrible thing whenever a non-white historical (or even fictional) figure is depicted by a white actor. Those people are entitled to their views. But even assuming for the sake of argument that it is a terrible thing, it doesn't justify the "see also". If there's a notable controversy over the particular film, then cite it and put it in the body. --Trovatore (talk) 08:29, 13 May 2017 (UTC)

re A Literary Nightmare

What's Homer Price got to do with it? Article doesn't seem to indicate anything. Herostratus (talk) 06:12, 1 June 2017 (UTC)

Yeah, that one's a little obscure. The connection is the story "Pie and Punch and You-Know-Whats", in which the poem is a central plot point.

"See also" is kind of a mess on this sort of thing in general. I especially dislike it when used tendentiously, as it is used to be in the article on the film The Last Temptation of Christ (there's there was a see-also to whitewashing in film, which strikes me as a backhanded way to sneak in a POV criticism without having to cite it).

I don't think anyone can accuse me of that in this case; at most a bit of whimsy. I couldn't really complain if you removed it. Or I suppose it could be mentioned at Homer Price, though finding a secondary source might be challenging. --Trovatore (talk) 06:22, 1 June 2017 (UTC)

Yes "See also" is odd. I had a discussion about this recently. It's not even clear to me after that what "See also" is for. It's supposed to be for stuff that is vaguely, but not closely, related to the subject of the article, for some reason. Still, I removed the Homer Price link (even though its I enjoyed reading that article) because it'd be head-scratcher for the reader I guess -- "why am I here"?" -- because the connection isn't mentioned in the article. If it's added that'd be different.

Speaking of whimsy, that article is on my watchlist because it was created by a vandal. He had apparently become enthralled with the poem in the article and was spamming it to random talk pages. I gave him (User talk:Mahk Twen#Talk page posts)the only vandal-warning in verse that I've seen. It was brought up at my RfA as both "for" and "against" reasons, heh. The editor then went on to make the article and then disappeared. But we got one article out of him. Herostratus (talk) 14:12, 1 June 2017 (UTC)

Can you recall what your final decision was in your old investigation?

Maybe that may be of help to me in my current investigation.

Additionally, may you also refer to this? HOTmag (talk) 08:18, 3 August 2017 (UTC)

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Help with getting MOS:TENSE established in an article

Hi, "Trovatore,"

I see that you're a somewhat frequent, or at least recent, contributor to the Manual of Style's talk page. I was wondering if maybe you'd be so kind as to offer your opinions and other help elsewhere as well. Have you been familiarized with MOS:TENSE? If so, what's your opinion about making sure it's applied? The MOS is a set of rules that applies to every article, correct? Would you please be so kind as to lend me your hand then?

Thanks if so, 174.23.158.54 (talk) 20:12, 8 September 2017 (UTC)

As long as I'm asking you for MOS help...

Also, as long as I have you here reading my request for MOS-establishment help, let me ask you for your opinion on some other things, okay?

Which to you is more accurate: calling abbreviations in which letters are pronounced individually, like a lot of initial abbreviations such as "CD," "ATM," and "LCD" are, as "acronyms," even though they are not (since they aren't pronounced as if they were just single words like "LASER," "SCUBA," "PIN," and "VIN," etc. are, and so those abbreviation examples are acronyms [even as "laser" and "scuba," and probably several others, have long been commonly lowercased]), or just calling them "initialisms" or "initial abbreviations" when they are indeed NOT acronyms?

Which to you is clearer: saying that a given model of computer or game system looks like just a "stereo" (which could be anything from a non-portable, traditional home stereo system, to a vehicle stereo system, to a tiny little MP3 player), or saying that it looks like a traditional home stereo system component?

And then, as a follow-up regarding systems that look like home-stereo equipment, if they are still computers, then which makes more sense: to compare them with other devices that look like just "computers" (even though these still are computers, so they look like their own unique type of computer), or to compare them against computers that look more like traditional computers?

Which do you believe is clearer: that when a specific computer-derived entertainment system can be converted into that computer by adding back specific peripherals such as a floppy disk drive like the derived-from computer model the system came with has, to simply say "disk drive" (which is ambiguous because it can refer to the CD drive that the machine already has, or to a hard disk drive which is only secondary to the floppy drive on those computers), or to be more specific by saying "floppy disk drive"?

Thanks for your opinions, and then we'll go from here,

174.23.158.54 (talk) 20:12, 8 September 2017 (UTC)

Hey, T, I've done my best to do the right thing and get my discussion going at talk:Commodore CDTV, but some trolls keep on deleting my discussion and all replies with it! Will you please help me out over there by restoring it and standing up for me, and then adding your own discussion? 75.162.224.110 (talk) 21:12, 9 September 2017 (UTC)

You have a right to know the rotating IP's belong to a banned user. See Wikipedia:Sockpuppet investigations/Stylized as "stylized" currently; formerly "stylizeD". Sro23 (talk) 00:32, 10 September 2017 (UTC)

Geekery

On that mess of a thread at WT:TPG, I wasn't sure what you meant by "a literal <br> inside <code> tags"; do you mean a line break in a code block when that block is visually rendered, a line break in the source that doesn't show up when the block is rendered, or the string "<br>" appearing in the code example, or something else? I've worked out pretty much every code-formatting thing to be worked out by this point (I write a lot of template documentation), so may know the solution regardless which question it is. PS: It should be <br />, or you'll be breaking people's syntax highlighters in source mode (never mind the fact that HTML5 does technically appear to permit <br>, without the /; gotta work with the tools we have).  — SMcCandlish ☺ ☏ ¢ ≽^ʌⱷ҅_ᴥⱷ^ʌ≼  13:43, 10 September 2017 (UTC)

I meant the literal string. I couldn't figure out how to escape it. I guess I know now; thanks. --Trovatore (talk) 19:35, 10 September 2017 (UTC)

Sho' thang. There are other options besides <br />, like <br />, and <br />, though the last works better in regular prose than inside a <code>...</code> block.  — SMcCandlish ☺ ☏ ¢ ≽^ʌⱷ҅_ᴥⱷ^ʌ≼  03:40, 12 September 2017 (UTC)

Semicolons

I just don't like them . Anyway, no big deal. Cheers - DVdm (talk) 21:50, 12 October 2017 (UTC)

Yes, we've had this discussion before, and I know you have that problem. Hope you get better . --Trovatore (talk) 21:52, 12 October 2017 (UTC)

Did we? Ha, that good to know. Perhaps you are particularly fond of them then. No problem... this must be one of those very rare occasions where I would agree to agree to disagree . Night! - DVdm (talk) 21:58, 12 October 2017 (UTC)

Quite: User talk:Trovatore/Archive04#Semicolon. Let's meet again in 2024 then... - DVdm (talk) 22:27, 12 October 2017 (UTC)

Don;t undo my close without a very good reason. [6] Do that again and it's off to ANi. Legacypac (talk) 05:08, 30 October 2017 (UTC)

Don't give orders, please. We can disagree about whether the material should appear, but an edit summary like "Don’t revert me" is entirely unacceptable. I think you may not like the outcome at ANI. --Trovatore (talk) 05:10, 30 October 2017 (UTC)

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Set theory

You reverted an edit, saying '(Undid revision 814336629 by 118.185.28.170 (talk) "wave or signal"? Not sure what this is trying to say.)' -- I think it was a joke. — Charles Stewart (talk) 08:34, 8 December 2017 (UTC)

Ah. Maybe. I don't really get it, but that's not surprising. --Trovatore (talk) 09:20, 8 December 2017 (UTC)

Actually I think it may be that the editor did not quite understand what a "wave" of excitement might be. Which makes me wonder if that sentence might need rewriting, using less metaphorical language? Paul August ☎ 14:48, 8 December 2017 (UTC)

Username

I do not impersonate anyone.--ASKechris (talk) 12:10, 9 January 2018 (UTC)

Hi ASKechris. I am not saying you are "impersonating" anyone. The word "impersonate" suggests intent to deceive, and I don't know your intent. I gave you the WP:IMPERSONATE link as a handy link to the policy, not to claim that you intended to deceive.

However the facts are that your username could suggest that you are Alexander S. Kechris, especially given that you have edited that article, and you are not he. I know that because I contacted him to ask.

Therefore your username is almost certainly not allowed. I hope you will change it. --Trovatore (talk) 20:33, 9 January 2018 (UTC)

Ah, now I see that you have put a note on your userpage saying that the name is "purely fictional". That is good, but probably does not solve the problem. The policy says you can do that if your real name is A. S. Kechris, which I suppose is possible, but strikes me as unlikely. --Trovatore (talk) 20:47, 9 January 2018 (UTC)

Utter nonsense. No way is my ASKechris the same as Alexander S. Kechris. I've reverted the incriminated edit. When opening this account I was not aware of nonsensic WP:IMPERSONATE. I will not change this user name for not wanting my e-mail address available to Wikipedia--ASKechris (talk) 21:05, 9 January 2018 (UTC)

Ah, too bad. It would be better if we could settle this amicably; we can always use good set theory editors, and you were quite right to point out readability problems at the ZFC article.

I will have to enter a notice at WP:UAA. I hope you will not take this personally. --Trovatore (talk) 21:15, 9 January 2018 (UTC)

Certainly I never said I was/is Alexander S. Kechris. If some bureaucrat can change it (say into ASKPireos, as I proposed) let it be done.--ASKechris (talk) 22:32, 9 January 2018 (UTC)

You don't have to give an e-mail address to request a username change. Just go to special:GlobalRenameRequest and fill out the form. The form does not ask you for an e-mail address. --Trovatore (talk) 22:35, 9 January 2018 (UTC)

@ASKechris: perhaps I was wrong — Wikipedia:Changing username does in fact say that a confirmed e-mail address is required to use that interface. I guess that must happen after you hit the "Request name change" button. But Wikipedia:Changing username/Simple is an alternative. --Trovatore (talk) 22:45, 9 January 2018 (UTC)

Bullets; thanks

Sorry, and given your being a regular, no ill will was assumed. The problem I have is presbyopia, even though I test as 20/20 with both eyes open, reading small, close-up print is difficult, and almost always both insert spaces between, before, and after my comments in the dialog box, since I find them inscrutable otherwise. Half of my edit count is effing typo corrections! Yours, -M

If you're using Chrome, you can make the text bigger by holding the Ctrl key and pressing +. (Well, actually it's =, on a standard keyboard, but it's easier to think of the up-and-down as control-plus and control-minus.) --Trovatore (talk) 20:23, 12 January 2018 (UTC)

I use Safari, which has the same ctrl+ option. The problem is brainiological, not sizic. I went to an auditory specialist, because I canNOT understand discussion when there is background noise. So she played these idiot sentences like "The sleb went down the snowy hill" and asked me what the actual message was. I was like, WTF!?!? My dog pulled me down the hill on slebs 40 years ago, you crazy... μηδείς (talk) 01:14, 13 January 2018 (UTC)

article: Republic

What gives you the right to delete hours of hard work? You said some is good and some is not then I would expect you to repair what you think is not good. Would you delete a thousand words of some one's hard work because they had a comma blunder, or maybe spelling error, or what threshold do you invent for your own subjective criteria. This point is not a rule of the Manual of Style. I'm sorry my friend but you have taken a very insulting action please restore my work and edit as you see fit. — Preceding unsigned comment added by DHT863 (talk) 20:49, 30 January 2018 (UTC)

No no no no. You need to slow down and convince people of what you're doing. It doesn't matter how long it took you. It matters whether you can justify it and get consensus. --Trovatore (talk) 20:50, 30 January 2018 (UTC)

Sir, there is already a statement on the talk page screaming about the horrible quality of the article. I fully agree with those comments. I worked hard, like I always do in other Wikipedia cases, to enter improvements. Additionally, you agree that some was good - that is a consensus. Now if you disagree on some points of my editing then you are perfectly free to correct those spots but common etiquette presumes you respect what you agree is good. I need you as a team member not an adversary. Please help to speed this along.DHT863 (talk) 21:20, 30 January 2018 (UTC)

No, you don't understand. There is no presumption that your changes are good. You are making complicated changes quickly, after having made comments that indicate you have a strong political position, though I haven't figured out yet exactly what it is. You cannot impose on others to vet your changes as quickly as you make them, and we don't want to allow WP:TIGER edits to slip through just because people don't immediately have time to read and check.

So it falls back to WP:BRD. You've made your bold changes, and they've been reverted. Now your move is to go to the talk page and defend them. --Trovatore (talk) 21:23, 30 January 2018 (UTC)

But you yourself said some were good? I know the difference between complicated and simple but maybe this is too much for you and the group. Nobody has the right to "vet" anything except judge the compliance to a neutral point of view. I don't want to impose on your time and think that you should respect my time and hours of work already invested. I do not have any political agenda. I do not belong to any political party. But I do believe in striving for the truth, goodness, and universal values that any person on earth can understand regardless of their preconceived notions or dogmas or crusades.

What is your authority? Who are the others? How have you and your group captured such authority? In light of the horribly poor quality of the article, lack of universal values, and absence of neutral point of view then how can you claim any legitimate authority in this case? It is incumbent upon you and your group to act now to edit and improve the article. It's obvious that your group has the manpower to do this. I could accept the consensus of your group making the needed improvements. I am sure you have a quorum to do that. DHT863 (talk) 22:50, 30 January 2018 (UTC)

I don't have a "group", and I don't have any "authority". No one else does either. That's not the point. The point is that you need to argue for your changes, rather than expecting others to argue against them. --Trovatore (talk) 00:10, 31 January 2018 (UTC)

DHT863 (talk) 00:40, 31 January 2018 (UTC) I'm afraid that is not how it works my friend. According to the talk page I am invited by Wikipedia: "Republic has been listed as a level-4 vital article in Society. If you can improve it, please do. This article has been rated as C-Class. Wikipedia says nothing about consulting you and says nothing about trying to convince you. Why should I when you summarily deleted all my hard work without any respect for even what you yourself said was good. You destroyed your credibility by doing that act. Is there any way you can apologize to me and restore my work for both of our edits? ---DHT863 (talk) 00:40, 31 January 2018 (UTC)

I destroyed nothing; it's all in the history. You just need to get consensus that it belongs in the article. See WP:CONSENSUS. Start making your case. --Trovatore (talk) 00:48, 31 January 2018 (UTC)

DHT863 (talk) 01:08, 31 January 2018 (UTC) If you did not destroy my work then where is it? Also, I entered discussion of "First Paragraph" in talk page for "Republic". ---DHT863 (talk) 01:08, 31 January 2018 (UTC)

Yes, you did — I don't agree with you but that's a good start. Your work is in the article history. Just click the "History" tabl. --Trovatore (talk) 01:11, 31 January 2018 (UTC)

Oh, actually I thought you were talking about "fifth paragraph". I haven't read the "first paragraph" stuff yet, so I don't know whether I agree with it or not. --Trovatore (talk) 01:13, 31 January 2018 (UTC)

I posted "Recommendations", "First Paragraph", and "Fifth Paragraph". Please review and comment. Thanks. ---DHT863 (talk) 18:34, 31 January 2018 (UTC)

Temptation

I see that you couldn't resist temptation. I was tempted to mention my philosophy-professor friend who uses Norwood's definition as the definition of philosophy, but didn't. I'm glad you posted, though: the point about empirical mathematics is quite good, and it had never occurred to me before, despite using simulations right at this moment to establish a mathematical conclusion that I can't get analytically. Anyway, do you know of a source that runs through a lot of these sorts of definitions of mathematics and explains what's wrong with them? Such a source could do a lot to improve Definitions of mathematics, which currently only presents the leading competitors, and without explaining the known problems with them. —Ben Kovitz (talk) 20:20, 12 February 2018 (UTC)

I don't know of any such source. Let me know if you find it, though. Sounds like something I'd like to read. --Trovatore (talk) 20:27, 12 February 2018 (UTC)

Walks on ordinals

Re this, there's no particular reason you can't work on the draft and eventually submit it for creation as a real article. The Todorcevic sockpuppet's contributions will be preserved as part of the article history, as usual. --JBL (talk) 18:21, 17 February 2018 (UTC)

@Joel B. Lewis: so first of all, I hope, when you say "Todorcevic sockpuppet", you're not implying that Todorcevic himself is responsible for these edits. I've seen that suggested, but it's utterly ludicrous. Even if you have no opinion on Todorcevic's ethics (which in my experience are impeccable), the BTZorbas contributions reflect a basic lack of competency in the subject (sorry to say that now that BTZorbas is blocked and can't defend himself).

I guess what I'm concerned about is that the draft may eventually be deleted, but still may influence any resurrection. Maybe that means I should go ahead and work on it. It's not the thing I'm most excited about, honestly, but it would be an excuse to learn the subject matter, 13 years after I should have.... --Trovatore (talk) 19:00, 18 February 2018 (UTC)

The construction that leads to "the Todorcevic sockpuppet" is a common one (e.g. 1, 2, 3), I don't think I need to defend its use. If eventually an article is created based on the draft, the the sockpuppet will be credited in the same way everyone else is (in the article history). If the draft gets deleted and eventually an article is created independently, it is not clear to me why any attribution would be needed. --JBL (talk) 02:08, 22 February 2018 (UTC)

That is fine. I was a bit touchy on the first issue because another contributor, generally a reliable one on math topics, had voiced the suspicion that the puppet belonged to Todorcevic himself. That suggestion shocked me a bit. --Trovatore (talk) 03:53, 22 February 2018 (UTC)

"short description" template

You have been adding the "short description" template at the beginning of a lot of articles. As far as I can see, it has no effect now. Why are you doing this? JRSpriggs (talk) 00:57, 22 February 2018 (UTC)

See Wikipedia:Short description and Wikipedia:WikiProject Short descriptions. As I understand it, Wikidata currently has per-language short descriptions, which show up for example in the Wikipedia mobile app (see screenshot at right). However these are considered less than ideal for various reasons, and I believe the plan is to replace them with the short descriptions embedded in the source of the WP articles themselves. My understanding is that this is intended to be done to every single WP article (though some may have deliberately empty descriptions). --Trovatore (talk) 01:35, 22 February 2018 (UTC)

Thank you for your reply. Perhaps you should mention it at Wikipedia talk:WikiProject Mathematics. JRSpriggs (talk) 16:26, 22 February 2018 (UTC)

I need your help...

Our article Goodstein's theorem claims, that this theorem - stating that every Goodstein sequence eventually terminates at 0 - is unprovable in Peano first order arithmetic. So (using Goedel numbers - I guess), Goodstein's theorem is expressible in the language of Peano first order arithmetic, so (as I guess) for every function F expressible in the language of Peano first order arithmetic, also the statement S(F) - stating that for every x the sequence (x, F(x), F(F(x)), F(F(F(x)))...) terminates at 0 - is expressible in the language of Peano first order arithmetic, am I right? If I am, then I wonder how this statement - S(F) - is expressible in the language of Peano first order arithmetic. For example, let F be the function F(x)=2x, so how can the language of Peano first order arithmetic express the (false) statement S(F) - stating that for every x the sequence (x, 2(x), 2(2(x)), 2(2(2(x)))...) terminates at 0? HOTmag (talk) 12:30, 25 February 2018 (UTC)

Using modular arithmetic and the Chinese remainder theorem, one can encode statements about finite sequences of natural numbers (of arbitrary length) by statements using only a fixed finite number of variables over the natural numbers. Then one just has to say that a_k has a certain relationship to a_k+1 for k in a certain range and constrain the first and last values of a. JRSpriggs (talk) 14:13, 25 February 2018 (UTC)

Axiom of choice

Hi Trovatore! I ask you to help me with this question. This seems to me a very interesting point about the axiom of choice, and I'd love to see this matter treated in an more encyclopedical and more didactical way. Haran (talk) 19:43, 1 March 2018 (UTC)

Diagonal argument 2nd talk page

The idea was to de-void the page. If you'd rather fix it yourself. The page is abandoned for a reason so I attempted to fix it. Victor Kosko (talk) 00:36, 29 March 2018 (UTC)

I see no reason the page should exist at all. You claimed that it "confuses the Wiki software" but gave no example. The talk/.../Arguments page has existed for years without a corresponding .../Arguments page, and it has never caused a problem.

In any case it has now been converted to a redirect, which seems fine. --Trovatore (talk) 01:17, 29 March 2018 (UTC)

April 2018

You currently appear to be engaged in an edit war according to the reverts you have made on FC Bayern Munich. Users are expected to collaborate with others, to avoid editing disruptively, and to try to reach a consensus rather than repeatedly undoing other users' edits once it is known that there is a disagreement.

Please be particularly aware that Wikipedia's policy on edit warring states:

1. Edit warring is disruptive regardless of how many reverts you have made.
2. Do not edit war even if you believe you are right.

If you find yourself in an editing dispute, use the article's talk page to discuss controversial changes; work towards a version that represents consensus among editors. You can post a request for help at an appropriate noticeboard or seek dispute resolution. In some cases it may be appropriate to request temporary page protection. If you engage in an edit war, you may be blocked from editing.
I will now inform the project as I asked you to. Cheers Walter Görlitz (talk) 23:18, 10 April 2018 (UTC)

MfD nomination of Talk:Cantor's diagonal argument/Arguments

Talk:Cantor's diagonal argument/Arguments, a page which you created or substantially contributed to, has been nominated for deletion. Your opinions on the matter are welcome; you may participate in the discussion by adding your comments at Wikipedia:Miscellany for deletion/Talk:Cantor's diagonal argument/Arguments and please be sure to sign your comments with four tildes (~~~~). You are free to edit the content of Talk:Cantor's diagonal argument/Arguments during the discussion but should not remove the miscellany for deletion template from the top of the page; such a removal will not end the deletion discussion. Thank you. ►К Ф Ƽ Ħ◄ 12:49, 19 April 2018 (UTC)

Invitation to WikiProject Portals

The Portals WikiProject has been rebooted.

You are invited to join, and participate in the effort to revitalize and improve the Portal system and all the portals in it.

There are sections on the WikiProject page dedicated to tasks (including WikiGnome tasks too), and areas on the talk page for discussing the improvement and automation of the various features of portals.

Many complaints have been lodged in the RfC to delete all portals, pointing out their various problems. They say that many portals are not maintained, or have fallen out of date, are useless, etc. Many of the !votes indicate that the editors who posted them simply don't believe in the potential of portals anymore.

It's time to change all that. Let's give them reasons to believe in portals, by revitalizing them.

The best response to a deletion nomination is to fix the page that was nominated. The further underway the effort is to improve portals by the time the RfC has run its course, the more of the reasons against portals will no longer apply. RfCs typically run 30 days. There are 19 days left in this one. Let's see how many portals we can update and improve before the RfC is closed, and beyond.

A healthy WikiProject dedicated to supporting and maintaining portals may be the strongest argument of all not to delete.

We may even surprise ourselves and exceed all expectations. Who knows what we will be able to accomplish in what may become the biggest Wikicollaboration in years.

Let's do this.

See ya at the WikiProject!

Sincerely,    — The Transhumanist   10:25, 21 April 2018 (UTC)

Beano

I have no knowledge of how the dietary supplement works, indeed I had never heard of it until I read the disambiguation page. Beano to me would be either the comic or the shindig, and I suspect the same would be trues of most other British people. DuncanHill (talk) 21:02, 25 April 2018 (UTC)

Ah, thanks for the info. I had been considering proposing a move that would make the page on the supplement the primary topic, but if that's the situation in the UK, it sounds like it's not a good idea. --Trovatore (talk) 21:23, 25 April 2018 (UTC)

Thank you very much

The RfC discussion to eliminate portals was closed May 12, with the statement "There exists a strong consensus against deleting or even deprecating portals at this time." This was made possible because you and others came to the rescue. Thank you for speaking up.

By the way, the current issue of the Signpost features an article with interviews about the RfC and the Portals WikiProject.

I'd also like to let you know that the Portals WikiProject is working hard to make sure your support of portals was not in vain. Toward that end, we have been working diligently to innovate portals, while building, updating, upgrading, and maintaining them. The project has grown to 80 members so far, and has become a beehive of activity.

Our two main goals at this time are to automate portals (in terms of refreshing, rotating, and selecting content), and to develop a one-page model in order to make obsolete and eliminate most of the 150,000 subpages from the portal namespace by migrating their functions to the portal base pages, using technologies such as selective transclusion. Please feel free to join in on any of the many threads of development at the WikiProject's talk page, or just stop by to see how we are doing. If you have any questions about portals or portal development, that is the best place to ask them.

If you would like to keep abreast of developments on portals, keep in mind that the project's members receive updates on their talk pages. The updates are also posted here, for your convenience.

Again, we can't thank you enough for your support of portals, and we hope to make you proud of your decision. Sincerely,    — The Transhumanist   08:47, 25 May 2018 (UTC)

P.S.: if you reply to this message, please {{ping}} me. Thank you. -TT

Categorization of von Neumann

Hi, Trovatore, sorry, you are correct, you didn't comment on this previously. I just confused in it my head with your attacks on me about an unrelated article. Sorry. Eleuther (talk) 00:10, 30 May 2018 (UTC)

If you are referring to the recent discussion on talk:real number, I did not attack you. I stated my own position forcefully, as Emerson might have counseled. But I said nothing about you. --Trovatore (talk) 00:13, 30 May 2018 (UTC)

True, sorry again. I should have said something like "your attack on my edit to an unrelated article." Cheers, Eleuther (talk) 00:40, 30 May 2018 (UTC)

I find the comment you made at Wikipedia:Categories for discussion/Log/2018 May 29 totally inappropriate for other reasons too. You should not be counseling others to disregard clear policy-based arguments, regardless of whether those comments came from participants in a discussion you personally find "toxic". (Yet somehow your counsel is privileged, as nominator, and should be listened to?) What matters is the strength of the arguments, not who makes them. You should collapse that entire thread. Sławomir Biały (talk) 13:28, 30 May 2018 (UTC)

Hi, Trovatore, I apologize for that angry interjection on your talk page, I didn't invite it. As for the present message, I would like to make a revision to my comment on the Cfd page. Part of it would be to change "all" to "most of" (to fix my factual mistake in your case), and to remove the word "toxic" (to satisfy Paul August). I would then remove the next three replies (including one of yours), on the grounds that they belong to a level of disputation that doesn't really belong on a CfD page. But I will only make this change if you and Paul August agree that it's okay. I sincerely hope you will agree. Thanks, Eleuther (talk) 17:38, 30 May 2018 (UTC)

@Eleuther: Since you called me out here, I will answer here (with apologies to Trovatore). Striking “toxic” would be an improvement, thanks for suggesting that. But the main point of your comment, that certain editor’s comments should be “discounted”, is problematic. You describe the editors who you want to discount as “disputants in the toxic discussion re von Neumann” But you don’t say which ones exactly, and you don’t say why.

You were a “disputant” in that discussion as well, but I presume you don’t mean for your own comments to be discounted? And what about Attic Salt, who supports the category, and to some extent the categorization, did you mean for them to be discounted? Or was it only the “toxic” ones (or if you strike “toxic”) then what? Only the editors who disagreed with you? Or what exactly? And by the way, if I am one of the editors whose comments you want discounted then why did you invite comments from me in the first place?

I would be fine with removing the entire thread. In lieu of that, I think hatting the thread, as Sławomir Biały has done, is the right thing to do. (P.S. Please feel free to respond to this on my talk page, and I would still like the answers to the questions I asked in that now hatted thread).

Paul August ☎ 19:40, 30 May 2018 (UTC)

Hi, Trovatore, I apologize again that this dispute has spilled over onto your talk page. I already asked Paul August to respond to the issue on his own talk page. I don't know why he saw a need to respond here. Sorry again. Eleuther (talk) 21:48, 30 May 2018 (UTC)

I hadn't yet seen your comment on my talk page, when I responded here. Paul August ☎ 21:56, 30 May 2018 (UTC)

Dylan

Re ref desk discussion. Reminds me of the time Dylan was asked what he meant by "people don't live or die, people just float" in the song "Man in the Long Black Coat" and he said "I just needed a word to rhyme with coat." --Viennese Waltz 06:38, 13 June 2018 (UTC)

Maybe I should look that one up. Honestly I mostly know Highway 61 Revisited (the album) and a couple other random songs. --Trovatore (talk) 06:41, 13 June 2018 (UTC)

Dis

I think I know what you were referring to on our talk page. One of the nurses here is an ex-Marine from California. He has told us many times that there was a song about a guy going to the enlisted club and being disked by a girl. I was a Marine also, but in South Carolina. I know what it means to disk. On the shooting range, if you miss the target completely, you get disked. That means that the person at the target end waves a disk on a stick to indicate that you missed. So, if I were disk you, it means that I'm telling you that you failed completely. It isn't exactly the same as disrespecting someone, but is similar. 209.149.113.5 (talk) 11:34, 29 June 2018 (UTC)

Thanks for letting me know!

Wait, what? There's a "person at the target end" at a shooting range? Doesn't sound like my dream job. --Trovatore (talk) 19:07, 29 June 2018 (UTC)

The Marines are known for doing more and more with less and less. There is no automation in the firing range. There is a pit at the target end where people stand, well below the firing line. The put targets on runners and pull them up using a chain and pulley system. When the shooter shoots, they pull down the target, mark where it was hit, and pull it back up again. As mentioned above, if the shooter missed the target all together, the target is sent back up and a disk on a stick is waved across the target. That is called "disking a miss." 209.149.113.5 (talk) 11:28, 2 July 2018 (UTC)

Re:RandNetter96‎

The user turned out to be a sock of a banned long-term abuser, who was reverting edits at random. So feel free to undo his reverts if you think it appropriate. Abecedare (talk) 02:56, 14 July 2018 (UTC)

Thanks for letting me know. I actually slightly prefer the article the way Rand left it, so I will probably leave well enough alone. If someone else wants to undo the revert, I'm OK with that too. --Trovatore (talk) 03:45, 14 July 2018 (UTC)

Yes, I see what you mean. It's a pretty even clarity of presentation vs technical precision call! Abecedare (talk) 03:53, 14 July 2018 (UTC)

WT:WPM

This has nothing to do with the request there. There are lots of venues (like this or this) on which such a question could be raised, and no particular reason to derail discussion on the topic of GA review. --JBL (talk) 21:30, 3 August 2018 (UTC)

I would be more inclined to support it for GA if it were named correctly. --Trovatore (talk) 21:32, 3 August 2018 (UTC)

That fact (which is entirely internal to you) does not make your comments on-topic. I think it would be good form for you to remove your irrelevant comment from that discussion. (I do not have any need to pursue this issue further than this, and if you do not wish to remove your comment that is up to you.) --JBL (talk) 21:38, 3 August 2018 (UTC)

I think it is on topic. --Trovatore (talk) 21:40, 3 August 2018 (UTC)

To be more explicit: The naming of an article is relevant to whether it should be promoted to GA. That fact is not internal to me. --Trovatore (talk) 21:41, 3 August 2018 (UTC)

To also be explicit: the thread is not about whether the article should or should not pass GA review. --JBL (talk) 21:43, 3 August 2018 (UTC)

Well, strictly speaking, that's a fair point. I'm hoping to get more eyes on this issue. I think the WikiProject is a reasonable resource for doing that, even if it's a slight divergence from the direct purpose of the original poster. --Trovatore (talk) 21:49, 3 August 2018 (UTC)

ZFC vs. ZF

Thank you for extending my initial and partial attempts to remove weasel words from the ZFC article. The article can be improved even more if we could:

• Add a citation that supports your statement that: ""ZF" unambiguously excludes choice, and is not synonymous with Zermelo-Frankel, which does not unambiguously exclude choice"
• Improve on the sentence "Today ZFC is the standard form of axiomatic set theory and as such is the most common foundation of mathematics" by summarizing some of the discussion in https://www.scientificamerican.com/article/infinity-logic-law/ about the treatment of CH with it's implied acceptance of ZFC.

I would appreciate your input and comments on these matters. Annette Maon (talk) 08:10, 6 August 2018 (UTC)

Hi Annette. Thanks for your note. I'm not sure where to cite the point about ZF unambiguously excluding choice — that's my experience, but I wouldn't necessarily state it so boldly in article space. I think it would be easy to cite the claim that ZF refers to a specific set of axioms, though, and these do not include choice.

I'll try to take a look at the other points soon. I need to sign off for now. Glad to have someone helping out with these articles. --Trovatore (talk) 08:13, 6 August 2018 (UTC)

I agree with you that ZF¬C is not a very interesting theory in itself and that mentioning it may give it undue weight. My intent was to mention it as a lead into the reason that the axioms of ZFC rather than ZF¬C "serve as the fundamental laws of mathematics" citing the Scientific American (SA) article and using it to replace the weasel words 'standard' and 'most common foundation' in the sentence I mentioned above.

The reason I mentioned ZF¬C at all is that the widest audience of readers may not be aware of the distinction between ZF and ZFC or its significance. I believe that Mentioning ZF¬C once before stating the dominance of ZFC can be a concise way to expose new readers to the issues without overwhelming them.

I believe that the addition of both AC and CH to ZF theory are notable enough to be mentioned in the lead for several reasons:

• Historical and philosophical: these are two axioms that both Godel and Cohen focused their initial efforts on.
• They are both extensively studied by Mathematicians.
• They need to be properly covered if we are eventually going to link to this ZF/ZFC page from the currently B-class, Top-importance article https://en.wikipedia.org/wiki/Mathematics

I was planning to select a few more quotes from the SA article to demonstrate that unlike ZF¬C, both CH and ¬CH are interesting enough to merit active research. Due to my incremental editing style, I did not have a chance to complete my intended edits before you reverted my ZF¬C additions. I think I will defer to your judgment on these matters and wait to see how you want to handle it. Annette Maon (talk) 04:43, 7 August 2018 (UTC)

help me

LuckyRacerNP (talk) 07:32, 27 August 2018 (UTC)

You don't state what it is you want help with. 331dot (talk) 07:53, 27 August 2018 (UTC)

Los Angeles

Los Angeles is a Megacity so your revert was unjustified. IWI (chat) 07:57, 3 October 2018 (UTC)

Hi User:ImprovedWikiImprovment. So yes, it's true that there are people who have come up with this notion of a "megacity", and that Los Angeles satisfies some definitions of the term.

But this term does not have the same status as "city" for describing human settlements. Cities have existed for millennia, and though there are different definitions of exactly what a city is, basically we understand what they are.

"Megacity", on the other hand, is a jargony neologism. Different people have proposed different definitions of which cities are megacities. To say that Los Angeles "is" a megacity means choosing some of those definitions as opposed to others.

Moreover, from an aesthetic point of view, it sounds absolutely terrible. It's dystopian and bleak. A megacity sounds like a place you absolutely would not want to live, a place of punishment. That's not the way I feel about LA, which I rather like.

So for all those reasons, I disagree with you. My revert was correct. I do not think we should be describing any cities as "megacities", but especially not LA. --Trovatore (talk) 15:22, 3 October 2018 (UTC)

What about New York City? I mean, your view is subjective: “it sounds dystopian”. The widely accepted definition is a city with an urban area of more than 10 million. IWI (chat) 15:25, 3 October 2018 (UTC)

It should also be removed from New York. It should not be used in any city infoboxes. But I don't care to press the point there; I'm not very interested in editing New York City. --Trovatore (talk) 15:28, 3 October 2018 (UTC)

File source problem with File:GimelUnicode.png

Thank you for uploading File:GimelUnicode.png. I noticed that the file's description page currently doesn't specify who created the content, so the copyright status is unclear. If you did not create this file yourself, you will need to specify the owner of the copyright. If you obtained it from a website, please add a link to the page from which it was taken, together with a brief restatement of the website's terms of use of its content. If the original copyright holder is a party unaffiliated with the website, that author should also be credited. Please add this information by editing the image description page.

If the necessary information is not added within the next days, the image will be deleted. If the file is already gone, you can still make a request for undeletion and ask for a chance to fix the problem.

Please refer to the image use policy to learn what images you can or cannot upload on Wikipedia. Please also check any other files you have uploaded to make sure they are correctly tagged. Here is a list of your uploads. If you have any questions or are in need of assistance please ask them at the Media copyright questions page. Thank you. ShakespeareFan00 (talk) 16:00, 23 October 2018 (UTC)

Done. --Trovatore (talk) 17:48, 23 October 2018 (UTC)

A Like-Minded Person

"Dreaming the same Impossible Dream"		The Like-Minded Persons' Club
		For displaying here common sense and uncommon good taste by agreeing with me or saying something I would have said if only I'd had the presence of mind, I hereby bestow upon you Provisional Membership of the Like-Minded Persons' Club. To qualify for Full Membership, simply continue to agree with me in all matters for at least the next 12 months. (Disagreements are so vulgar, don't you think? And, as Bruce Chatwin said, Arguments are fatal. One always forgets what they are about)

Thanks JackofOz! I shall treasure it. --Trovatore (talk) 21:58, 17 November 2018 (UTC)

ArbCom 2018 election voter message

Hello, Trovatore. Voting in the 2018 Arbitration Committee elections is now open until 23.59 on Sunday, 3 December. All users who registered an account before Sunday, 28 October 2018, made at least 150 mainspace edits before Thursday, 1 November 2018 and are not currently blocked are eligible to vote. Users with alternate accounts may only vote once.

The Arbitration Committee is the panel of editors responsible for conducting the Wikipedia arbitration process. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose site bans, topic bans, editing restrictions, and other measures needed to maintain our editing environment. The arbitration policy describes the Committee's roles and responsibilities in greater detail.

If you wish to participate in the 2018 election, please review the candidates and submit your choices on the voting page. MediaWiki message delivery (talk) 18:42, 19 November 2018 (UTC)

You've got mail

Hello, Trovatore. Please check your email; you've got mail!
It may take a few minutes from the time the email is sent for it to show up in your inbox. You can at any time by removing the {{You've got mail}} or {{ygm}} template. Maknongan (talk) 14:34, 31 December 2018 (UTC)

Jacobus

Yes, even I. But membership of the Like-Minded Persons' Club does not require concord in all matters, so you can rest easy.  :) -- Jack of Oz ^{[pleasantries]} 01:34, 8 January 2019 (UTC)

"Sourceable criticism"

HOTmag's self-indulgent, cranky bloviating is not "sourceable criticism", it is self-indulgent, cranky bloviating. The material you uncovered is directly counter to the goal of having the reference desk be a place where meaningful information can be exchanged. If HOTmag wants to go on at length about how 0^{-1} = 0, let him get a blog like all other cranks; please please please don't encourage posting of garbage. (Anyone who wants to read his nonsense can of course still click the "uncover" button.) --JBL (talk) 19:08, 20 February 2019 (UTC)

Unfortunately HOTmag went on a bit beyond what was really necessary to address the issues with the purported solution x=0, I'll grant you that. But the initial criticism was justified. --Trovatore (talk) 19:11, 20 February 2019 (UTC)

That is an extremely generous way to describe perhaps 10 paragraphs of utterly useless self-regarding bs. The reasonable point is covered by the brief, on-point response of the OP to Kusma. Consequently, there is 0 value to anyone in anything HOTmag added to the conversation. Anyone who wants to read pointless cranky bloviating can still do so by the act of clicking one single link. There is no excuse for setting the standard of discourse on the RefDesk so low. --JBL (talk) 03:56, 21 February 2019 (UTC)

• No need to hide the source I gave.
• No need to use personal attacks, like "self regarding nonsense...valueless crud" (in the edit summery ), or "crankery" (at the Ref-desk), or "self-indulgent cranky bloviating...garbage" (here).
• Actually, the OP asked for a solution. An editor suggested $0^{0}$ as a solution. I gave a source from Wikipedia for the controversy over $0^{0}$ as a solution. The editor - who suggested $0^{0}$, and me - who disagreed, have explained our opposing positions about $0^{0}$ as a solution, using reasonable mathematical arguments (rather than "cranky" ones) for each position, without being "self indulgent", nor "self regarding", but rather with having full respect to each other's position (that's why I used the phrase "in my view" - just in order to make sure that it's my view only - so I don't want to impose it on whoever disagrees with it), so please give us the same respect.
• Further, Travatore is a witness here: I'm ready to grant you one thousand USD, within three days after you let me know the address (in USA) for sending the money, provided that before you do that, you will do - within 24 hours from now - one of the following:

1. Mathematically prove that what I've written at the Ref-desk this week, is "nonsense" or "garbage".

2. Mathematically prove that $0^{0}$ can be a solution to the OP's question.

3. Mathematically prove that the identity $0^{x}=0$ for every integer $x$ (including non-positive $x$), is inconsistent with arithmetic (or with set theory), while assuming the domain of discourse is that of the integers (hence without assuming the controversial continuity of the function $a^{0},$ at every $a$, i.e. including at $a=0$), and without assuming the controversial identity $a^{0}=1$ for every $a$ (i.e. including $a=0$), and without assuming the controversial identity $a^{-x}=1/(a^{x})$ for every $a$ (i.e. including $a=0$). By "arithmetic" I mean, the traditional definition of addition and multiplication, along with the traditional definition of the Power function: $a^{x}=a^{x-1}a$ - and $a^{1}=a.$

4. Find out any logical (or arithmetical) fallacy, in my proof at the Ref-desk, that $0^{0}=0$ (and that actually $0^{x}=0$ for every integer $x$), while accepting Frege's requirement that every function ("every" - so including the Power function whose traditional definition is mentioned above), should be applied in the whole domain of discourse - wherever possible consistently (Here I assume the domain is that of the integers).

Trovatore, are you ready to be the judge, to determine if I have to pay one thousand USD as I've promised (on condition that...)? HOTmag (talk) 11:21, 21 February 2019 (UTC)

Hi HOTmag. I'm afraid I have no interest in mediating such a contest. --Trovatore (talk) 21:11, 21 February 2019 (UTC)

Not a mediator, but rather a judge, who just has to determine (by "yes/no") if I have to pay. Afraid? So...without a judge. AFAIC, I'm not afraid, to risk one thousand USD, because I'm sure they won't be able to fulfill any of the four conditions I've set forth. HOTmag (talk) 22:26, 21 February 2019 (UTC)

0^x = 0 if x>0; 0^0 = 1; and 0^x is undefined if x<0. JRSpriggs (talk) 04:38, 22 February 2019 (UTC)

Wrong. As for x=0, see 0^0. As for x<0, see the hidden paragraph at the Ref desk. HOTmag (talk) 11:07, 22 February 2019 (UTC)

Construction of Real Numbers

Is there an inconsistency you would like to point out on the changes to Real Numbers? — Preceding unsigned comment added by JPMural (talk • contribs) 20:10, 3 April 2019 (UTC)

Please open a discussion at talk:real number rather than on my talk page; this is a discussion about the article and others may wish to weigh in. --Trovatore (talk) 20:13, 3 April 2019 (UTC)

Canonicity of the construction is presented in section 6 and 7. The Von Neumann and the Zermelo-Fraenkel ordinals are embedded in our construction; one being the powers of 2, and the others being the powers of 2 minus 1. The It is further said that numbers cannot be specifically defined, that we cannot put our finger on an object and say "this is the number 3". In Sections 6 and 7 we prove this actually can be done, for example with trees and sets187.189.208.183 (talk) 19:43, 8 April 2019 (UTC).

I don't see how that is different from any of the standard constructions. "Canonical" means that it's the only possible representation that adequately captures all the relevant features. It has to be strictly more complete, accurate, natural, or all three, than any other possible representation; if it isn't; it's not canoncial. Does the paper prove that? Can you point me to where? --Trovatore (talk) 03:41, 9 April 2019 (UTC)

This discussion of canonicity goes beyond that in Canonical form, which deals with canonicity with respect to a class of representations. Here, it is as if you are interested in a Platonic form that represents the true essence of the phenomenon. I'd say, for instance, that continued fractions constitute a representation of reals that deserves the name canonical, and that claim does not prejudice claims to canonicity of quite different representations.

I have a different complaint about the paper. It has many definitions and axioms, but only one theorem. This asserts that the operations on naturals/reals "exist and are well-defined". This falls rather short of asserting that they satisfy any particular algebraic properties. Am I missing something? — Charles Stewart (talk) 17:33, 9 April 2019 (UTC)

The "Platonic form that represents the essence of the phenomenon" is exactly what seems to be claimed. I am skeptical. --Trovatore (talk) 17:41, 9 April 2019 (UTC)

Ive pointed out where you can search to see canonicity. If you choose to make criticism on something you havent read, it is a waste of my time. Im not going to write it here or justify in a few lines, beacuase its already written and published. Any mistakes pointed out or real corrections are welcome.187.189.208.183 (talk) 15:22, 11 April 2019 (UTC)

To be honest you have not made the case that it is worth my time to actually read it. --Trovatore (talk) 16:37, 11 April 2019 (UTC)

comments

Several users has endorsed the block and whatever your personal philosophy or bold scepticism, it could only be you are not completely aware of what has happened. Or I'm going to be sorry I posted here. cygnis insignis 18:26, 30 June 2019 (UTC)

What I understand has happened is that someone committed a horrific crime, and that someone else posted a video of that crime. Wnt made it easier than it otherwise might have been for other users to find the video. Have I missed something relevant? --Trovatore (talk) 18:42, 30 June 2019 (UTC)

Yes, you have, and overlooked the other endorsements of those who are also aware. Is it curiosity or a wish to muse over ethics that prompts you to ask? And use that to dispute the block on that page in the process. Are you picking up the tone in my messages? cygnis insignis 19:24, 30 June 2019 (UTC)

I consider Wnt to be a valuable contributor, whom I would like to see continue contributing. I do not feel that there has been adequate process behind the block, particularly an indef block. "Tone" is difficult to judge accurately in a text format. Perhaps it would be more efficient to simply state what you believe I have missed. --Trovatore (talk) 19:39, 30 June 2019 (UTC)

Read the tone as brittle. If you don't think there was justification for the "necessary" block, or have no faith in those who did, there are avenues for review process. I never want users blocked, quite honestly, so for goodness sake give some thought to this and read up on how the unmentionable came to do the unthinkable. cygnis insignis 19:59, 30 June 2019 (UTC)

"The unmentionable." The Christchurch shooter? The videographer, who apparently agreed with the shooting? Or Wnt? "The unthinkable." The shooting, the video, or making it known how to find the video? These are rather different things, or at least so they seem to me. Again, if you believe that I have missed something, it would be most efficient simply to say what it is. --Trovatore (talk) 20:09, 30 June 2019 (UTC)

• Concerning process: "I do not feel that there has been adequate process behind the block, particularly an indef block." So far in process, there have been two declines to the unblock requests so at least two other admins have commented but all of those who monitor Category:Requests for unblock would have also seen it and have remained silent. To continue process, Wnt may either file another unblock request for the admins to review as he has previously done or he may appeal to the community at AN by requesting that the admins copy his next appeal there for him. The latter comes with a higher degree of risk however as a indef block endorsed by the community becomes a community ban. If that happens then any future unban requests must either be made to the community at AN or to Arbcom per WP:UNBAN.
   — Berean Hunter (talk) 22:09, 30 June 2019 (UTC)
  • Forgot to add a quantitative assurance that his unblock requests have been seen and it isn't being forgotten or ignored. Approximately one third of his pagewatchers have also visited at the time of this writing.
     — Berean Hunter (talk) 22:21, 30 June 2019 (UTC)

Grammatical "myths"

In a recent edit summary, I said,

"Whose" should have a person, not an entity like infinity, as antecedent.

You replied,

"Whose" absolutely does *not* need a person as an antecedent. That's a myth and a total misunderstanding of the word

That's two claims: that the putative rule is a myth and that it's a total misunderstanding.

According to the "usage note" in this source, using "whose" with inanimate antecedents has been complained about since the 1700s though prominent authors including Shakespeare have been employing this usage since the 1300s. However, the source also refers to a survey in which only 44% of a sample of English speakers approved of the sentence "The EPA has decided to dredge the river, whose bottom has been polluted for years." That's only one survey and hardly conclusive, but I think it provides a weak reason, at least, to avoid such a construction in Wikipedia.

As regards the putative rule being a myth, I'm genuinely unclear what that could mean. It is commonly thought that grammatical prescriptions are right or wrong, and calling mine a myth seems to imply that it's wrong. There's even a Wikipedia article Common English usage misconceptions which maintains that certain usages thought wrong are sometimes not so, i.e. that they're sometimes right. I find it difficult, however, to condemn usages out of context so long as they are intelligible and unambiguous. I do think that some are best avoided in certain contexts, including Wikipedia articles, because readers are likely find them so jarring that they divert attention from the subject matter to the language in which it is expressed. On that basis, I recommend against the use of "whose" under discussion. I likewise think that sentences in Wikipedia should not begin with "And", while condoning that usage elsewhere.

Total misunderstanding? I take "whose" to be the possessive form of "who". Do you disagree?

While I have your attention, I compliment you on your edits to the Infinity article, which are invariably well done. Also, your use of asterisks for emphasis in an edit summary is something I might try. I have been regularly using capitalization for the purpose.

Peter Brown (talk) 01:22, 17 November 2019 (UTC)

@Peter M. Brown: You say "whose" is the possessive form of "who". Correct but incomplete. It is also the possessive form of "which" and "that" (as a relative pronoun), which otherwise would not have possessives. --Trovatore (talk) 02:34, 17 November 2019 (UTC)

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Elegant

Didn't want to clog up the other discussion with what I admit is pedantry... but what I mean is this:

You drew a distinction between some people preferring a "modern, plain-English style" or a "traditional, elegant" style. This is a loaded distinction, like saying that some people prefer "sausages", while others prefer "delicious ice cream" (implication: sausages are not delicious). Or suggesting that while some men like "brunettes", others prefer "sexy blondes" (implication: brunettes are not sexy).

Why would anyone not prefer a more "elegant" style? Answer - they don't. Everyone thinks their style is more elegant. I know that's your point, but it isn't supported by your actual wording.

Anyway, I understood your point nonetheless, I just wanted to clarify what I was getting at with my cheeky comment and emoticon, and I hope you're having a pleasant morning/afternoon/evening wherever you are. Popcornduff (talk) 23:59, 22 November 2019 (UTC)

Agreeeth

Pretabulated at [7]... -- AnonMoos (talk) 00:25, 7 January 2020 (UTC)

Los Angeles (snow image)

Per [8]. I remember consensus for previous image, where is consensus for this new image? Link please. Subtropical-man (✉ | en-2) 22:12, 27 February 2020 (UTC)

Subtropical-man You may "remember" consensus, but it was never officially found to be consensus, with three editors supporting the image if you look in the discussion. Some of the opposition to that image was based on technical flaws that are not apparent in the newer image. --Trovatore (talk) 22:15, 27 February 2020 (UTC)

There were objections/opposes for snow. This new image show snow, so. Subtropical-man (✉ | en-2) 22:21, 27 February 2020 (UTC)

There was never a consensus against snow. There were opposes for snow, but also supports. --Trovatore (talk) 22:22, 27 February 2020 (UTC)

There were no supports for snow, the user to whom do not mind snow does not mean automatic support for snow. By the way, but topic of change of skyline is disputed and controversial, new image generally no different from the previous one - which has been removed from article (the same shot and snow), so - must to be consensus. Subtropical-man (✉ | en-2) 22:29, 27 February 2020 (UTC)

There was at least one support specifically for snow, namely mine. The new image is significantly different from the older image, because it does not have the graininess and other technical flaws, which was part of the rationale for removal. --Trovatore (talk) 22:32, 27 February 2020 (UTC)

Do not base 100% on previous discussion / consensus. This is new image, this is new edit - chahge of skyline, this is new case but this is still disputed and controversial. For disputed and controversial images, where there is clear opposition or even edit-war, before new changes must to be consensus per Wikipedia:Consensus. Subtropical-man (✉ | en-2) 22:38, 27 February 2020 (UTC)

The Bends

Agreed on the page move... but we now have a bunch of wikilinks to fix. I'll do some but any help appreciated. Thanks. Popcornfud (talk) 22:10, 29 February 2020 (UTC)

OK, I've done some too. --Trovatore (talk) 07:47, 1 March 2020 (UTC)

@Popcornfud: barring reverts or new additions, I've finished article space. I think that's the main thing. I probably wouldn't touch talk or user talk, but up to you if you want to. If you feel like tackling File space or Wikipedia space, those are probably worthwhile, though I doubt they're critical. --Trovatore (talk) 08:12, 1 March 2020 (UTC)

Great, thanks. Popcornfud (talk) 15:47, 1 March 2020 (UTC)

"Wayne Chiang" listed at Redirects for discussion

An editor has asked for a discussion to address the redirect Wayne Chiang. Since you had some involvement with the Wayne Chiang redirect, you might want to participate in the redirect discussion if you wish to do so. Prisencolin (talk) 23:47, 26 April 2020 (UTC)

Concerning: Cantor's first set theory article

Hi, Trovatore. I wish to congratulate you on your choice of a sentence to delete from the lead section of Cantor's first set theory article. Obviously, it's a high profile sentence that you disagree with. But it's also a sentence that has started to bother me: Putting dates of 2014 and 2015 in the lead section might be read as dating the research, which would be inaccurate and not relevant for a lead. However, I hadn't decided how to modify it. Your elimination of this sentence solved the problem for me. So, thank you. The other sentence you removed leads into the following sentence so it emphasizes what I am saying. I like that sentence, but I don't think it's worth our time to argue over it. By the way, when I started working on this article, my work was mainly based on my Math Monthly article, Georg Cantor and Transcendental Numbers, which starts off by stating "Conflicting statements have been made about Cantor's proof of the existence of transcendental numbers". The Wikipedia article with its new title has led me to add Cantor's various related proofs. So the focus of the Wikipedia article has broadened to include more mathematics.

Now we come to your statements: "There is not a disagreement. There is not a controversy. It's such a simple question that everyone agrees. They just phrase it differently." I think you may have a point of view that I might learn something from, so I have a few questions I'm interested in.

First, I looked up "disagree" on my computer and it states that "disagree" means "have or express a different opinion". For example, Oscar Perron and Abraham Fraenkel disagree because one of them states that Cantor's proof for the existence of transcendental numbers is a non-constructive proof while the other states that this proof is constructive. So Perron and Fraenkel have and express a different opinion. However, I do agree that it's not a controversy, which is defined as a "disagreement, typically when prolonged, public, and heated." Mostly one side ignores the other so it never gets heated. Are your definitions of "disagree" or "controversy" different from mine?

Now for your statements that I find a bit cryptic but very interesting: "It's such a simple question that everyone agrees. They just phrase it differently." Please explain why "It's such a simple question". What is the question? Also, why do you think that everyone agrees? Finally, how do they phrase it? Thank you, RJGray (talk) 16:31, 5 May 2020 (UTC)

@RJGray: What I mean is that the modifications of the argument to produce a specific real number are so straightforward that it is not really plausible that Perron and Fraenkel actually dispute it. Either they haven't seen it (Fraenkel I think died quite a long time ago so that's a bit of a different case), or they consider it to be enough extra argument that it's no longer really "Cantor's argument". Neither of those possibilities is very interesting, and neither constitutes a real disagreement about whether the argument gives an explicit real. The second possibility is, at most, a disagreement about what counts as "Cantor's argument", which is much less substantive than the language made it sound. --Trovatore (talk) 20:03, 5 May 2020 (UTC)

——— Changes to article ———

Hi Trovatore. I have retitled the section "The disagreement about Cantor's existence proof." The new title is "A misconception about Cantor's work," which comes from Akihiro Kanamori's article "Set Theory from Cantor to Cohen." I like "misconception"—it's a great improvement over "disagreement" and it's in a quote that I can reference. Also, I made some smaller changes to the rest of the section.

Thank you for clarifying for me what mathematicians may mean by "Cantor's proof". Perron references both Cantor's 1874 article and his 1891 diagonal argument article since he uses the diagonal argument instead of Cantor's 1874 argument. Since the proof Perron gives uses a combination of Cantor's arguments from his 1874 and 1891 articles, it appears clear to me that he is using "Cantor's proof" to credit Cantor with all the arguments in the proof. If mathematicians commonly do this and someone has written this down, please send me a reference to it. I give evidence that this is how he is using "Cantor's proof" in the footnote at the end of the 3rd paragraph, but a reference would be very good to have.

By the way, I had restricted "Cantor's proof" to Cantor's published proof because "proof" is singular and I was thinking more about the history of the proof. This caused me to restrict what I viewed as "Cantor's proof" to be a proof that Cantor published. I never thought about the possibility that mathematicians might be accustomed to a different usage of "Cantor's proof." Thank you for pointing this out to me.

If you want to see my changes, they are located at User:RJGray/Sandbox2. It consists of the new section "A misconception about Cantor's work" and a two-sentence change to the 2nd paragraph of the Lead. I plan to put these changes into the article in about a week and a half.

Thanks for your help, RJGray (talk) 11:07, 7 July 2020 (UTC)

Is P ∧ ¬P logically possible?

Spurred by your statement that virtually any state of affairs that is logically possible can be described mathematically (which I doubt on the basis of cardinality considerations, but this aside) I had a look at our article Logical possibility. <Insert facepalm>. Please see Talk:Logical possibility#Is P ∧ ¬P logically possible?.  --Lambiam 20:15, 3 June 2020 (UTC)

Why does multiplying by a decimal equal a smaller number and dividing by a decimal is a larger number? I can never wrap my head around this. For example: 100 × .5 = 50 but 100 ÷ .5 = 200. How

— Preceding unsigned comment added by 2601:2c3:4201:d70:8545:7e48:9462:35b6 (talk • contribs) 19:20, 7 July 2020 (UTC)

Hi 2601:2c3:4201:d70:8545:7e48:9462:35b6. I'm really not sure I'm the best person to answer this sort of question, but I'll give it one try. If you don't like my answer you could try at WP:RD/Math

Suppose you have a positive number, say 7.234, and you multiply it by something bigger than one. It increases, right? You get something bigger than 7.234, agreed?

And if you multiply it by one exactly, it doesn't change, it just remains 7.234, correct?

So what should happen if you multiply it by something less than one?

Division is similar. --Trovatore (talk) 03:23, 8 July 2020 (UTC)

Central Business District

Your attention is called to the addition of this display to the article on the Central Business District, Los Angeles (1880s-1890s). Do you have any feelings, for or against? Discussion should take place on that article's Talk page. Thanks. BeenAroundAWhile (talk) 18:01, 16 August 2020 (UTC)

Ordinal Number

You reverted the simplification and page templates from ordinal number. The technical tag leads to the following statement: The content in articles in Wikipedia should be written as far as possible for the widest possible general audience.

I think that the idea that 'ordinal numbers' are a purely technical concept that is only understandable by mathematitions pretty agains the concept of Wikipedia. I agree it needs technical elements. What I did agree with is that the first paragragh should be so complex that even someone with a passing understanding of the concept should have to battle through the definition.

Ideally, this article should have a layman's explanation as the first paragraph of the article, and ideally each section. Mathematics is for everyone -- let's find a way of making it more accessable?

Please edit, not revert the work that I have done on this article.

86.11.51.106 (talk) 07:01, 28 September 2020 (UTC)

Hi 86.11.51.106. I'm pretty sure you're looking for the concept described at ordinal numeral. The ordinal number article is about the concept initiated by Georg Cantor. It is already quite accessible for the subject matter and does not require the tags you added. --Trovatore (talk) 15:48, 28 September 2020 (UTC)

The vast majority of it is unsourced. It looks like a bunch of maths graduates got together and wrote it. I definately think that tag needs to stay 86.11.51.106 (talk) 17:06, 29 September 2020 (UTC)

Sourcing is a separate issue. It is not too technical, so it doesn't need the technical tag. It's probably not unsourced either, but I'd have to check more carefully to respond to that. --Trovatore (talk) 17:37, 29 September 2020 (UTC)

Natural numbers

(a) — Preceding unsigned comment added by LMSchmitt (talk • contribs) 21:05, 30 October 2020 (UTC)

(a) Thanks for your message.

(b) I removed the contentions {1,2,3...} even though I do think as a professional mathematician that this is hilarious. In math the most common setting is IN={1,2,...} and INo={0,1,...}. Some computer scientists let IN include the 0. Starting from 0 is sometimes a bit better in regard to binary words and tensor products, and FOR-loops in C-programming. ;-)

(c) Sorry, the statement of the FTA is such a nonsense that it needs to be removed immediately. Take the equation in one complex variable:

exp(z)=0

That is an equation in one complex variable, but it cannot be solved since exp(z) is always non zero. The FTA is about such equations as

z^5 + b z^4 + c z^3 + d z^2 + e z + f = 0

a polynomial equation for which, in general, no formula for the solution exist, but a complex solution IS always guaranteed by the FTA. That's a very strong statement about IC.

(d) IR is actually invented to have limits of rational approximations of Sqrt[2]. Or similarly, Pi as the area of the unit circle. Continuous properties can also be studied in IQ which has a metric (distance). This part of the article is only semi-correct.

(e) I moved the statement about FTA closer in the writing where IC is introduced. In the text, it seemed lost context-wise where it was.

(f) I find it good that the symbols IN...IR..IC are introduced even for laymen. I introduced them to resume the discussion after the statement of FTA. LMSchmitt 21:48, 30 October 2020 (UTC)

Hi LMSchmitt. Please don't lecture me about what's "most common in math". I have also been a professional mathematician (Ph.D. UCLA, postdocs at UNT and York (Toronto)). In my field, set theory, natural numbers most typically include zero; the other convention is basically an archaism. --Trovatore (talk) 22:02, 30 October 2020 (UTC)

We've had an agreement to leave this ambiguous since 2006: Talk:Mathematics/Archive 7#Naturals, Nonnegatives, Positives. Computer scientists often prefer to talk of unsigned integers, which is the term favoured in the C standard. I don't know why the ISO standard prefers the naturals to include 0, but if I had to guess it is because the main use of integers in the physical sciences is to represent finite cardinalities, so the definition of Nat that includes 0 is more useful than that which excludes it. — Charles Stewart (talk) 20:48, 17 January 2021 (UTC)

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math and maths

I don't want to start a whole new discussion on the topic, but could you point me to the reasoning behind not having these two redirected words at the top of the Mathematics article? To me, it would seem natural to have them, but apparently it is not the consensus - and narrowing the search for them in the talk archives is a bit frustrating. I'll watch here... --John (User:Jwy/talk) 18:08, 11 December 2020 (UTC)

They just aren't needed. They're informal short forms. They cause problems because if you have them, you have to decide which one goes first. If you don't have them, you haven't lost any content that's actually about mathematics, and the whole controversy goes away. --Trovatore (talk) 18:13, 11 December 2020 (UTC)

I used to be heavily involved in the Disambiguation world and expected to see them bolded near the top. I'd still like to see them there, but life's too short. Thanks! --John (User:Jwy/talk) 18:47, 11 December 2020 (UTC)

"Chigger" listed at Redirects for discussion

A discussion is taking place to address the redirect Chigger. The discussion will occur at Wikipedia:Redirects for discussion/Log/2020 December 30#Chigger until a consensus is reached, and anyone, including you, is welcome to contribute to the discussion. MB 22:01, 30 December 2020 (UTC)

Non-zero sum game

I hyphenated the word "non-zero" in the opening sentence of the article on hyperreals quite deliberately, because it just places a little more emphasis on the fact that infinitesimals cannot take a zero value (which is of course what motivated the development of the hyperreals to begin with). In my view, a reader is more likely to grasp that this is a significant fact if they are reading two distinct syllables rather than ones which blend into each other. If one was going on immediately to expound on this point, then I would agree that it is less important, and it is less necessary to hypenate the word nonstandard as already by that point the reader has probably got the idea that there's something a bit unusual about the hyperreals!! Understanding is surely more important than concistency here, therefore I am changing it back and would be grateful if you could leave it as it is. Thank you, however, for making an improvement as you saw it.

Edwin of Northumbria (talk) 23:12, 15 January 2021 (UTC)

Murder

Hi Mike,

Our discussion was instructive to me. Thank you! By the way, your UNT website is no longer available, but I found you anyway :-)

PS. I live in Poland, but I want to master the English language before I die ;-) 85.193.228.103 (talk) 00:52, 20 February 2021 (UTC)

Mistaken ping

Apologies for my inadvertent notification at Wikipedia:Reference desk/Science. Although, of course, any input of yours is still welcome:) --DB1729 (talk) 18:29, 8 June 2021 (UTC)

Email

Hello, Trovatore. Please check your email; you've got mail!
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Train Song: "By"

Sorry, Trovatore, that I'm so late in replying, but if you recall, in March (2021) you commented on the List of Train Songs talk page that the use of "by" in referring to "recorded by" struck you as inappropriate or unusual. I wasn't sure what I would use in its place that wouldn't be too long - for example, "recorded by" - but then I noticed that this is the "form" used on AllMusic. For example, if you use AllMusic's search box to look for a song, each song found will be in this form: "Wabash Cannonball" by Mac Wiseman or "Orange Blossom Special" by Bill Monroe. Thinking about it more, I realized "by" is used in this context all the time, by deejays, for example, as in "And here's 'She Loves You' by the Beatles" or in literature, "1984 by George Orwell". All that said, I understand how the usage may have seemed incorrect, and thought you deserved the courtesy of a reply. P.S. I'm posting a shorter version of this on the Train List talk page. Allreet (talk) 21:36, 26 November 2021 (UTC)

@Allreet: I just re-read this and realized I hadn't quite gotten my point across. My point was not that "by" is wrong, but that it implies a writer credit, not just a performer credit. That is, 1984 is indeed "by" George Orwell, but "Me and Bobby McGee" is "by" Kris Kristofferson, not Janis Joplin or Roger Miller. Kristofferson also performed it, but it's "by" him because he wrote it. --Trovatore (talk) 01:53, 3 March 2022 (UTC)

@Trovatore: Understood. Originally I got part of your point, obviously not all of it. I spent decades as a writer often working with other writers, and all hell could break loose between us now and then over some of the smallest words of all, prepositions. Yeah, the Beatles both wrote (well, at least two did) and recorded the songs, so no matter. Not the same in nuance when authors differ from the artists. I'll rethink the usage because such precision is important. Allreet (talk) 12:35, 3 March 2022 (UTC)

About removing piped link on 0.999...

I think your change to 'Informal mathematics', the title to the connecting article, makes sense and reduces ambiguity. There seems to be some talk in that article's talk page about changing it (back?) to 'Naïve mathematics' or maybe something else entirely (I haven't weighed in yet, but I may), the objection appearing to be the usage of the word 'informal', because in the academic context mathematics can be "informal" but not "naïve". If they change it, we would have to change the link to the page as well, but I suppose that's just the way of things! Anyway, I had known that adding the diaeresis would be controversial I would probably have offered more of an explanation for the change! I hope you are having a great day! Kind regards. - --Webspidrman (talk) 23:08, 28 February 2022 (UTC)

Brief thoughts:

1. While I don't think the diaeresis over the i is actually banned, I suspect general sentiment is against it, especially among the folks who specialize in working on the MOS.
2. In any case, there will be redirects, and I don't see any strong reason not to use a redirect in a "See also". Using piped links seems very strange though.
3. Finally, "See also" isn't that important and probably not worth the time we've already put into discussing it. --Trovatore (talk) 23:37, 28 February 2022 (UTC)

Tematagi

It was "Antipode of Mecca" until recently (see article history). AnonMoos (talk) 09:19, 5 December 2021 (UTC)

Yes, I changed it. --Trovatore (talk) 18:32, 5 December 2021 (UTC)

People in their 50s dying of old age

People in their 50s dying of old age

William Hartnell was about 55 years old when he played the original incarnation of the Doctor in Doctor Who and maybe 58 in his final story. While Richard Hurndall was about 72 or 73 when he played him in the 20th anniversary story The Five Doctors and David Bradley was 75 in the 12th Doctor's (Peter Capaldi) two final episodes The Doctor Falls and Twice Upon a Time. Here are images of 55 year old actors, 58, 72-73 and 75. And the cause of the First Doctor's regeneration was old age. 86.130.4.167 (talk) 18:37, 25 May 2022 (UTC)

Can people die if they've become old, weak and worn out in their 50s? And did the original Doctor look about mid-50s, 60s or 70s? 86.130.4.167 (talk) 19:24, 26 May 2022 (UTC)

ANI thread related to discussion in which you participated

Hi, just notifying you of this ANI thread connected to a discussion on the MoS talkpage. Boynamedsue (talk) 17:13, 23 June 2022 (UTC)

A Dobos torte for you!

7&6=thirteen (☎) has given you a Dobos torte to enjoy! Seven layers of fun because you deserve it. To give a Dobos torte and spread the WikiLove, just place {{subst:Dobos Torte}} on someone else's talkpage, whether it be someone you have had disagreements with in the past or a good friend.

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Lightface analytic game

Hey,

Was wondering where Lightface analytic game came from. I'm unable to find anything on the topic. Thanks! Ovinus (talk) 22:18, 3 October 2022 (UTC)

I created that stub when I was very new to Wikipedia — I wouldn't do it today. If you're interested in the math, start looking at the refs in zero sharp (maybe Moschovakis or Jech). If you're interested in the term, it's a combination of lightface and analytic set, together with a "game" in the sense of determinacy. As for what to do with the stub, I'd probably merge it into zero sharp. --Trovatore (talk) 22:27, 3 October 2022 (UTC)

Thanks for the clarification! I'd appreciate it if you could merge it yourself; I'm set-theoretically challenged. Ovinus (talk) 18:55, 4 October 2022 (UTC)

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Help!

Sir I want to edit wikipedia but when I add content someone always reverts it what should I do? John2900 (talk) 11:12, 8 January 2023 (UTC)

My little humble award from one mathematician, though I am certainly not as professional or high-level as you are, to another.

		Scholarly Barnstar
		Academicians should also be responsible for laypeople or amateurs directly, apart from working only in their academic world. Making efforts to enhance mathematical content here is so very kind of you. I wholeheartedly congratulate you. MaxineLund (talk) 23:41, 22 August 2023 (UTC)

Thank you MaxineLund! --Trovatore (talk) 00:01, 23 August 2023 (UTC)

Units

Aloha Travorte,

Here is the quote from Magnetic moment#Units

I could not figure out how to respond on the article Talk page, so responded to you directly.

Units

The unit for magnetic moment in International System of Units (SI) base units is A⋅m², where A is ampere (SI base unit of current) and m is meter (SI base unit of distance). This unit has equivalents in other SI derived units including:

$$\mathrm {A\cdot m^{2}} ={\frac {\mathrm {N\cdot m} }{\mathrm {T} }}={\frac {\mathrm {J} }{\mathrm {T} }},$$

where N is newton (SI derived unit of force), T is tesla (SI derived unit of magnetic flux density), and J is joule (SI derived unit of energy). Although torque (N·m) and energy (J) are dimensionally equivalent, torques are never expressed in units of energy.

Thank you for taking the time to explain your answer more fully. I agree that the example from Jc3s5H had inconsistent units. I agree with most of your points, but never mentioning a unit associated with a variable is contrary to many Wikipedia articles, IEEE requirements and the style used in many cited references, and likely a requirement for publication.

I made another pass an believe that the magnetic sail article links to many other articles that use units with variables, and only a few do not. If this is to be changed, it is much larger than a single article. Dmcdysan (talk) 18:14, 24 October 2023 (UTC)

You said there were units associated with variables in that text. I do not see any variables there at all, with or without units. --Trovatore (talk) 18:46, 24 October 2023 (UTC)

References

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Proposed deletion of Fallen Leaf Lake (disambiguation)

The article Fallen Leaf Lake (disambiguation) has been proposed for deletion because of the following concern:

Disambiguation page not required (WP:ONEOTHER). Primary topic article has a hatnote to the only other use.

While all constructive contributions to Wikipedia are appreciated, pages may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the {{proposed deletion/dated}} notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the page to address the issues raised. Removing {{proposed deletion/dated}} will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Shhhnotsoloud (talk) 17:46, 2 February 2024 (UTC)

Doppelgänger

I blocked a new account Trovatore1, whom I assume is not actually you. DMacks (talk) 19:29, 5 February 2024 (UTC)

True, that is not me. Seems like a borderline case though; it's not clear that it's an attempt to impersonate me. I'm not super familiar with all the nuances of the username policy. --Trovatore (talk) 20:01, 5 February 2024 (UTC)

Thanks for the confirmation. This part of the policy is about potential effect, not confirmed intent. So it's not important whether the person behind that account is trying to impersonate you, merely that it is a very close username that could lead to confusion by others. DMacks (talk) 21:56, 5 February 2024 (UTC)

‭ב₂‬ in heading

{{lro}}ב<sub>2</sub>{{popdf}}  --Lambiam 21:24, 5 May 2024 (UTC)

Thanks. In general I've found that putting templates in headings results in edit summaries with incorrect anchors, but clicking on yours seems to work. Is that a recent fix in the software, or are these templates specifically designed for the purpose? --Trovatore (talk) 21:31, 5 May 2024 (UTC)

Well, now when I click on my own edit summary, it does not seem to work. --Trovatore (talk) 21:32, 5 May 2024 (UTC)

Super

Cool talking with you. Maybe it continues. As for links... I welcome your interest. 1. Red links do not belong in tables. What is the point? 2. As for them being anywhere, two points. a) They exist because when an article is removed the words are still there. Point blank. b) If they are to be more permanent then what is the criterion for such? Also there are other things on here (Wikipedia) which could (should) be solved. Among them two are the use of images and permissions. People on here object to any usage of first names when disambiguating names too. Delectable1 (talk) 00:56, 12 July 2024 (UTC)

Hi Delectable1. Please respond on your own talk page. When I initiate a conversation, I watchlist the user talk page of the other person (at least for a while) so I will find out if you respond. --Trovatore (talk) 01:11, 12 July 2024 (UTC)

Regular cardinal

Hi Trovatore, if you get time, could you make sure my recent edits to Regular cardinal are ok? I'd appreciate it! Rich (talk) 13:48, 23 July 2024 (UTC)

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