Wikipedia:Reference desk/Archives/Mathematics/2014 May 4

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May 4

continuing discussion about Naive set theory

continuing discuission of "http://en.wikipedia.org/wiki/Talk:Naive_set_theory#Definition_of_.22naive_theory.22". So you claim that out of the Limberg-definition and the claim that it's consistent follows that 1=0? Sorry, I can't follow you. I can't imagine how this could have been done. 79.252.242.192 (talk) 22:06, 4 May 2014 (UTC) Thomas Limberg (Schmogrow)

So you wanna know, what the word "well-defined" means. It means that any definition of a set M doesn't contain or lead to an inconsistancy about M. How do you wanna show an inconsistancy, when I exclude inconsistancies by definition? (it's night now in Germany, so I probably won't post in the next ours) 79.252.242.192 (talk) 22:01, 4 May 2014 (UTC) Thomas Limberg (Schmogrow)

"So you claim that out of the Limberg-definition and the claim that it's consistent follows that 1=0?"

Not really, but close enough. If the claim that it is consistent is provably true from your Limberg-definition, then, yes, 1 = 0 as well as 1 ≠ 0 will follow.

If you want other (and probably better) answers, I'd recommend you to write down your Limberg-definition here and ask a proper question, not continue an argument from an article talk page after having been reverted. Correctness or consistency of your Limberg-definition was not the issue when you were reverted, nor was it the issue on the article talk page. You might be able to raise it as an issue here though, but probably not by just continuing an argument from the talk page (that I probably should have refrained from commenting on, ah well, arguments can be plenty of fun). YohanN7 (talk) 22:51, 4 May 2014 (UTC)

You want the Limberg-definition of sets. Here we go:

A set is a well-defined collection of objects. A collection C is well-defined means that the definition of C doesn't contain or lead to an inconsistency about C. The objects are called the elements or members of the set. Objects can be anything: either elementary objects or other sets. Elementary objects are numbers, people etc.. They are no sets themselves. There is no requirement that a set be finite. If x is a member of a set A, then it is also said that x belongs to A, or that x is in A. In this case, we write x ∈ A. An empty set (with no elements) is possible, often denoted Ø and sometimes $\{\}$.

Hope I didn't forget anything. But I think it is consistent. You wrote "If the claim that it is consistent is provably true from your Limberg-definition, then, yes, 1 = 0 as well as 1 ≠ 0 will follow.". Erm, normally I would say that definitions are not allowed to contain or lead to inconsistencies. So when "the claim that it is consistent is provably true" from my Limberg-definition then 1 = 0 will not follow cause when it is proven to be consistent you can't follow an inconsistency out of it. So I think that you mean that my Limberg-definition contains or leads to an inconsistency. Sorry, I don't see anything wrong. You have to show me, what you think is wrong. I haven't added a definition of a set, yet. And I don't see a contradiction in the definition of the "set"-term (Limberg-definition) itself. And even if I would add set definitions, then inconsistencies were excluded by the Limberg-definition. (Hey, YohanN7, where are you from, cause it's morning now in Germany and you didn't answer yet, (-: ... hm, it's 5 1/2 hours ago now since you posted. Are you busy, asleep or do you not know, what to write, cause my remarks are so convincing (or other reason)?) 79.252.242.192 (talk) 01:53, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

I have told you one thing that is wrong with your theory, and where to read about why (Gödel's incompleteness theorems). I'm not going to spend more time on this because you seem just about knowledgeable enough to not ever believe in your nonsense. You are trolling. YohanN7 (talk) 10:27, 5 May 2014 (UTC)

You are talking BS! I have told you one thing that is wrong in your entry! And that is: When it is proven that my theory is consistent then you can't say that it leads to 1 = 0. Do I have to explain you what the word consistent means or what?! It means that the theory does not lead to wrong statements!!!!! 93.197.8.254 (talk) 10:52, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

Just to be clear, YohanN7 is referring to Godel's second incompleteness theorem:

For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent. (quoted from Gödel's incompleteness theorems)

If you believe that your theory includes even a little bit of standard mathematics (e.g. number theory) then it cannot include a proof of its own consistency without being inconsistent. I hope you won't ask for the specific problem with your theory which rules out a consistency proof- this is a typical gambit of people who refuse to believe impossibility proofs when they imply disappointing results. If you don't believe in Godel's incompleteness theorem then nobody here will be enthusiastic about debating it with you. Staecker (talk) 11:57, 5 May 2014 (UTC)

"When it is proven that my theory is consistent ..."

The thing is, if your theory is a set theory, this proof from your theory will exist if and only if your theory it is inconsistent. Such a proof does lead to 1 = 0 in your theory. Once more, I urge you to read Gödel's incompleteness theorems. (And lower your tone.) YohanN7 (talk) 12:02, 5 May 2014 (UTC)

"Just to be clear, YohanN7 is referring to Godel's second incompleteness theorem", yeah he said that, but just to be clear, I did not refer to it. I just talked about my definition. "The thing is, if your theory is a set theory, this proof from your theory will exist if and only if your theory it is inconsistent.", so you do assume that my definition is inconsistent. Good that we've cleared that. But I've already told you that definitions are only allowed when they are consistent. So I just would have to discard my definition and come up with a weaker one. You say that a set theory with a little arithmetic and the claim that it is consistent would lead to an inconsistency. Does that mean, the theory is inconsistent or the consistency is just not provable? And then, what about the consistency of Zermelo-Fraenkel set theory? Can we say anything about that? 93.197.8.254 (talk) 12:27, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

Ah, ok, I think the consistency of ZFC is just not provable. But then the 2. Gödel incompleteness theorem only says that my definition (with some arithmetics) cannot be proven consistent. It doesn't mean it was inconsistent. Hm, ok, but then what is your problem with my definition? 93.197.8.254 (talk) 13:01, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

If you include enough sets to get a consistency proof, but make sure never to include any sets which would make it inconsistent, then you will be including very few sets. In particular your theory will not be sophisticated enough to express basic number theory. So likely there is no such thing as "my definition (with some basic arithmetics)". As soon as you allow in number theory (I guess that's what you mean by arithmetic), you will have introduced inconsistencies. This must be true, again, by Godel's second incompleteness theorem. Staecker (talk) 13:10, 5 May 2014 (UTC)

Häh?! You're talking crap, don't you?! "If you include enough sets to get a consistency proof... ", I didn't know I would get a consistency proof just by adding sets. "but make sure never to include any sets which would make it inconsistent", that what I've said several times already. "then you will be including very few sets. In particular your theory will not be sophisticated enough to express basic number theory.", yes it will since ZFC does too. Or doesn't it? "As soon as you allow in number theory (I guess that's what you mean by arithmetic), you will have introduced inconsistencies.", no, it just says, that consistency can not be proven! 93.197.8.254 (talk) 13:38, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

I'm beginning to feel like you're not listening (no need to say "I told you so", Yohan) so I probably won't respond any more than this. Set theory proofs require sets to be constructed and discussed- if you only allow certain kinds of sets, then this will only allow certain statements to be proved. Conversely if you require that a consistency proof will exist within your system, then this will require certain types of sets to exist in your set theory. If you insist that your theory has enough sets to make a consistency proof, but also no inconsistencies, then this is a major restriction. Godel's theorem says that such a system can be consistent, but will be not be sophisticated enough to express basic number theory. You objection "yes it will since ZFC does too" is false because ZFC does not contain a proof of its own consistency. No mathematically useful version of set theory can, because of Godel's theorem. Staecker (talk) 13:46, 5 May 2014 (UTC)

No need to say "I'm beginning to feel like you're not listening". I've listened very closely and given you replies to your statements. I'm beginning to feel like you don't wanna listen to what I say. "if you only allow certain kinds of sets, then this will only allow certain statements to be proved.", tell me something I don't know. I've made several comparisons to ZFC and now I do it again, just for you: ZFC only allows certain kinds of sets, either. So in ZFC only certain statements to be proved are allowed, either. So what do you wanna tell me. I don't see a difference to ZFC here. "Conversely if you require that a consistency proof will exist within your system ...", do you mean the word "well-defined" in my definition, or what? "If you insist that your theory has enough sets to make a consistency proof", you mean to formulate a consistency proof? I don't insist that my set definition (the "set"-term definition I mean) has to be proven consistent, since you told me about Gödel. "because ZFC does not contain a proof of its own consistency", neither does my definition. 93.197.8.254 (talk) 14:43, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

Ok- I will reckon it as progress if you've come around and are now agreeing that your system cannot contain a proof of its own consistency. Staecker (talk) 16:45, 5 May 2014 (UTC)

I cannot remember stating that my system could contain a proof of its own consistency and I'm not going to. But ok... 93.197.8.254 (talk) 17:41, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

I see a breakthrough. Nice.

The problem with your definition is that it was invented yesterday afternoon. It has not been tested for inconsistencies for more than 100 years - as has naive set theory (which really is informal ZF set theory, give or take an axiom or two). Therefore, the latter is more suitable for the article. YohanN7 (talk) 13:09, 5 May 2014 (UTC)

The solution is simple: Start testing it and give it some time. My definition has a clear advantage. I said that several times already, too. It is a general set definition in comparison to ZFC! You can actually answer (or at least try to) the question, if the statements which are the axioms of ZFC are true or false. For example, is there an empty set? Yes, there is! When A and B are sets, then is there a set that contains the elements from A and those from B together? Yes, there is! And so on. That's why I say that my definition is better than ZFC. 93.197.8.254 (talk) 13:38, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

Yes, you can perhaps start to add axioms to your theory by asking "Does this addition yield inconsistencies?" If no, then add it (as a theorem). The problem is that you will not get very far because your system of axioms (actually theorems in your theory) will soon be large enough that you can't answer the question "Does this ney addition yield inconsistencies?" any longer.

If you could, then I'm afraid Gödel is going to bite you in the ass again. But believe me, this approach has been very very thoroughly investigated in axiomatic set theory over the years. YohanN7 (talk) 13:59, 5 May 2014 (UTC)

Oh one more thing. I see that new subthreads appear above with sometimes nasty formulations. We have been extremely patient with you, but don't push it too far. I don't personally mind even if you call me an idiot (because I am an idiot), but others aren't as insensitive. Your are balancing on a thin edge. YohanN7 (talk) 14:08, 5 May 2014 (UTC)

Sorry, what shall I do? I shall add theorems like "this addition yield inconsistencies"? Which addition? Do you mean the statements which are axioms in ZFC or do you mean definitions of sets? I don't get it. 93.197.8.254 (talk) 14:43, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

You might try this: Whenever you don't understand something, acknowledge that as a fact, not as that something being incorrect. Try once again to understand. And again. Sooner or later you will pick up something true and useful – just like you finally actually understood bits and pieces of what Gödel 2 has to say about the consistency of ZF. (I commented on that as a breakthrough above, not for your theory, but for YOU.)

Instead of me or anyone else patiently explaining again to you, try to think about what Gödel 2 has to say about your latest claim (your "simple" solution of above). Then think about it again. And again. If you still think you don't understand, them come back and ask here. There is no point in explaining more clearly, because you are not going to accept it unless you discover it almost all by yourself.

Whenever someone tells you that you are wrong, you need to be even more thoughtful before vigilantly responding in a rude way. Given your apparent level of knowledge and experience with the subject, it is close to a certainty that you, in fact, are wrong when anyone here (except me, told you I'm a lunatic) so suggests. YohanN7 (talk) 15:19, 5 May 2014 (UTC)

You make a fundamental mistake here. Suppose I would say that 2+2=4 and 10 people say I'm wrong, then I still don't give in. But I ask every single one of them for his "solution". Then someone will say 2+2=5, someone will say 2+2=7 and someone will say 2+2=3. Then they will notice that they have to rethink their results. Sorry, that's a pseudo-argument for me. 93.197.8.254 (talk) 15:38, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

I think this Youtube video fits to this situation: "http://www.youtube.com/watch?v=16OrRGwwQ_0". It says: "A seven nation army couldn't hold me back.". 93.197.8.254 (talk) 16:09, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

"Given your apparent level of knowledge and experience with the subject", another fundamental mistake. You've noticed it by yourself already. When I need to know something, I look it up. I only have to know the stuff that is important for this discussion. It's not nesseccary for me to have a deep knowledge of for example Gödels theorems. You said the consistency of my definition cannot be proven and I didn't disagree, although I didn't check Gödels 2. theorem. I said I don't insist on such a proof. Why would I inform myself about Gödels theorem, when I don't insist on such a proof. I said ZFC doesn't have such a proof either. So I don't see a problem here. 93.197.8.254 (talk) 15:58, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

And since you're talking about knowledge and experience, I got a 3. price in the country round of the German Mathematics Olympiad when I was at school. 93.197.8.254 (talk) 16:13, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

Ill respond to one of your items. Then I'll tell you my opinion.

"You said the consistency of my definition cannot be proven and I didn't disagree." Yes, you disagreed several times. Violently.

Similarly for your other items. You simply don't listen.

You should have stayed in school. What do I know? Now you are just a combination of a thinks-he-knows-it-all-crank and a troll. YohanN7 (talk) 16:25, 5 May 2014 (UTC)

"Yes, you disagreed several times. Violently.", sorry I can't remember a single time. Would you be so kind and give the source to at least one of your assertions? Oh, and lower your tone! 93.197.8.254 (talk) 16:57, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

Sure, this page and Talk:Naive set theory. YohanN7 (talk) 17:01, 5 May 2014 (UTC)

Oh boy, you're not very familiar with scientific work, heh? I have to explain you everything, heh? Ok, here we go: When you state something, you have to give me the exact place where I can find it, not only a wikipedia page (they can be very long). And you should give a citation (like I did so many times when I answered you). Why is that so hard for you? I thought I would deal with people here who have some skills! 93.197.8.254 (talk) 17:18, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

I haven't seen any scientific work done in these pages. But, since you ask for citations, every post of yours containing 1 = 0, and/or one in response to one of mine that contains 1 = 0.

I am resigning from this discussion. I should have done that a long time ago, but I saw some light in the tunnel somewhere in the middle. It's gone now because you have reverted from mostly being a crackpot to only trolling and being generally unpleasant. You can call me everything and anything, I don't care very much, but I don't enjoy it enough to continue. YohanN7 (talk) 17:45, 5 May 2014 (UTC)

You wanna resign, fine with me! See I've given you the exact source of my assertions so many times and when I ask you once for it, you're not able to give it to me. You're hallucinating. Stop calling me troll! You're the troll here! I think I'vew found what you mean. I said a single time "I think it is consistent". And nothing more! 93.197.8.254 (talk) 18:05, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

To the curious reader. Here is one quote from Limberg's posts containing 1 = 0 in response to being informed that a set theory proving its own consistency is inconsistent (Gödel's second incompleteness thm):

"You have to do something! YohanN7 is starting to insult me! He writes that when a theory is consistent then he can show that it leads to 1 = 0, though. That's so stupid! Stop him!"

It should illustrate pretty clearly that he either has no clue about what he is talking (is a crank (probable)) or is just in here for the fun of it (is trolling (less probable, but not entirely impossible)). YohanN7 (talk) 23:51, 5 May 2014 (UTC)

Ok, now I'm sure, you are retarded! It says "when a theory is consistent...", I didn't even refer to my definition. And I've already told you I was not referring to Gödels theorem, either. I think you gave me a misinterpretation of Gödels theorem and I just pointed that out! Oh yeah, and you're the crackpot cause you're hallucinating! 93.197.47.238 (talk) 04:16, 6 May 2014 (UTC) Thomas Limberg (Schmogrow)

Limberg wrote what he wrote it in response to this (which is not a misinterpretation of Gödel):

In fact, the very moment you claim you have a definition of set theory, free of paradoxes—as a consequence of the definition itself, your claim (if true) implies that your theory is inconsistent, able of proving 1 = 0, hence containing paradoxes. (YohanN7)

Most posts from Limberg has been of the same nature, not only the ones directed to me. Part insult. Part denial. Part intentional misquotes and part intentional lies so that he can hide his ignorance and continue his journey. In this case, he has later on, sort of, admitted he knew nothing about Gödel for the reason that he didn't need to. See the posts following his sudden insight that ZFC isn't provably consistent. Now, he justifies calling me stupid (and adds retarded) with that he was correcting my misinterpretation of Gödel's second theorem. YohanN7 (talk) 09:42, 6 May 2014 (UTC)

What you say is wrong, you're the liar and insulter!!! You hide your ignorance and continue your journey. "Limberg wrote what he wrote it in response to this", the word response is ambiguous. It was a reaction, not an answer. I've pointed that out already several times when I wrote, I didn't refer to Gödels theorem. How many times do I have to repeat it? You're slow on the uptake. I said once "I think it's consistent" and didn't repeat it. Why would I, the topic of the discussion changed. You misinterpreted Gödels theorem, didn't change your mind and insulted me! Don't complain about me insulting you back! 93.197.47.238 (talk) 13:16, 6 May 2014 (UTC) Thomas Limberg (Schmogrow)

And now, replies aren't supposed to be "responses" or "answers", they are reactions. I never said either that your "reactions" refer to Gödel's theorems. In fact, they couldn't possibly have, because you didn't (and still don't) know about Gödel's theorems, but they were replies reactions to my posts. More insults, now "liar". Where do I misinterpret Gödel's teorems? For reference, I wrote

In fact, the very moment you claim you have a definition of set theory, free of paradoxes—as a consequence of the definition itself, your claim (if true) implies that your theory is inconsistent, able of proving 1 = 0, hence containing paradoxes. (YohanN7)

You did, however, misinterpret it my friend, in your response reaction. I didn't insult you yet, but I might consider doing so.

Slightly off topic: Do you still think we should rename what is today called "naive set theory" in our articles to "Thomas Limberg (Schmogrow) set theory" as you did in your first edits of that article?

It is possible that it would be the right thing to do. Write something about that on the article's talk page please. YohanN7 (talk) 13:49, 6 May 2014 (UTC)

"Where do I misinterpret Gödel's teorems?", ... oh now I have it ..., "If the claim that it is consistent is provably true from your Limberg-definition, then, yes, 1 = 0 as well as 1 ≠ 0 will follow.", Gödel doesn't say that the consistency claim has to be provably true. He just says the claim has to be made! That's how you misinterpreted it.

Moreover, "I didn't insult you", yes you did (crackpot)! Denial, you're a liar! 93.197.47.238 (talk) 15:53, 6 May 2014 (UTC) Thomas Limberg (Schmogrow)

No, Gödel says that if the consistency claim is provably true from the premises, then it is in actuality false (hence not actually provably true). But don't feel bad about this. Many people, even more brilliant than you, as has been mentioned by @Staecker:, feel intimidated. A consistency claim being made isn't enough to prove an inconsistency (it is only entirely pointless). It is enough though, if you can prove the consistency from your premises. Then your theory is provably inconsistent and useless.

I called you a (crank = crackpot) because I believe you are one. It is not an insult, and not a lie. You want to name set theory after yourself and don't know about Gödel. Yet you are intelligent enough to propose an actually sensible tentative definition of what you think set theory ought to be. When directed to fallacies of what you thought was a perfect definition, when these fallacies are pointed out to you, then you hide in a shell and furiously refuse (including insulting people, changing old arguments into something else, etcetera) to acknowledge others actual century-old knowledge. This makes you a crank (or crackpot, which is a synonym) by definition of the term.

You still have the option to contribute to Wikipedia (and even science), but first, you need to dig out of your hole. YohanN7 (talk) 16:55, 6 May 2014 (UTC)

Stop insulting me!!! I wanted a serious discussion, but you're not able to do this! "because I believe you are one" is not sufficient!!!!! You have to know it!!!!! That's very unscientific! That's religion or something. Stop it!

I may edit my posts afterwards, but I do it directly after I posted them and very quickly (within 2 or 3 minutes). You don't check my posts every minute, do you? So it's not so relevant!

Maybe the spot I've given you was not the one where you misinterpreted Gödels theorem. That was just a sudden idea. (see I immediatly revise myself, when something turns out to be wrong what I said). Gödels 2. theorem demands e.g. "basic arithmetical truths". I told you already, I haven't added any set definitions, yet. I don't think this condition is fulfilled. And even if I would add sets or definitions in number theory, they would have to be well-defined. Thus, inconsistencies are excluded by definition!

You say "If the claim that it is consistent is provably true from your Limberg-definition", what does "from your Limberg-definition" mean? I mean if you (or better: I) wanna show the consistency of my definition then of course you (or I) have to make use of it. Does the "from" mean that other stuff (definitions or something) is excluded? Probably not, I have to define sets and maybe I shall define arithmetic operations so that the demand for number theory is fulfilled. 93.197.47.238 (talk) 18:26, 6 May 2014 (UTC) Thomas Limberg (Schmogrow)

You have done a mistake. You told me about Gödel but that was just an answer to my question. You didn't say you wanna refer to it or apply it when you made your assertion. I always suppose, when someone wants to use definitions or views from a source that differ from the ones you have when you're not so much into the topic then this one tells me that. Otherwise it would be unscientific. So now I ask you explicitely: Do I have to have a deeper knowledge of Gödels theorems to understand what you said or is my common knowledge sufficient? Staecker said just later in the discussion that you refer to Gödel, so I suppose the answer is yes. But that's not always so. A source might proof statements which don't contain redefined terms, too. So you have to tell me when that's the case. When you've used terms in your assertion that Gödel has given a different meaning than the commonly known one, you should tell me that (I asked you about the "from" explicitely already). Ok? 93.197.47.238 (talk) 18:26, 6 May 2014 (UTC) Thomas Limberg (Schmogrow)

I'm not insulting you my friend. Just being blatant with you.

You are now retreating to that "Maybe the spot I've given you was not the one where you misinterpreted Gödels theorem" where I (YohanN7) supposedly misinterpreted Gödel was a " sudden idea", therefore not an actual reply (or even a reaction?) of yours because I (YohanN7) didn't get Gödel wrong exactly there (but supposedly somewhere else) — hence not even a reflection of yours, just a "sudden idea". Interesting. Wouldn't it be more honest to say you have no clue?

Right, you haven't added any set definitions yet, except for numbers, people, bananas, ...being not sets (see previous post of yours above, not too sure about the bananas). This is quite conflicting with the usual notion, where numbers always are sets (and bananas optionally are, depending on the particular theory).

You still don't get what Gödel has to teach you. This is only natural, since you knew nothing about this two days ago when you started your journey. No Limberg definition in the world will help I'm afraid.

When you exclude inconsistencies by definition, then you are limiting yourself to a non-set theory if you want it provably consistent. Study hard.

My advice is still to jump off that train of yours. It's going to take you nowhere good. YohanN7 (talk) 18:43, 6 May 2014 (UTC)

Your last paragraph of above is extremely hard to understand. It begins with the mandatory insult: "You have done a mistake..." Then you ask if you need to understand Gödel. You assume this is so (supported by reference to @Staecker:. Then you conclude that you don't need to understand Gödel - or what do you conclude? The paragraph is incomprehensible, sorry. YohanN7 (talk) 18:43, 6 May 2014 (UTC)

"The paragraph is incomprehensible", no it's not! You're just not able to read my posts (anymore). "I'm not insulting you my friend", yes you are, "crackpot" is an insult! Furthermore, I was actually talking about set definitions like "M := {x|x is even}". So you mean the "set"-term definition. Well, ok, you can interprete it that it contains number theory. Let's suppose for the numbers that are mentioned in the Limberg-definition are arithmetical operations defined. "you hide in a shell and furiously refuse ... to acknowledge others actual century-old knowledge. This makes you a crank", you're hallucinating again. I said several times, you misinterprete Gödels theorem. I didn't say Gödels theorem was wrong!!! "When you exclude inconsistencies by definition, then you are limiting yourself to a non-set theory if you want it provably consistent.", when there is {}, or even {0} and {1}, then there are sets there and I don't see any contradiction. So it is a set theory! 93.197.19.94 (talk) 04:02, 7 May 2014 (UTC) Thomas Limberg (Schmogrow)

First a piece of advice. Don't clutter your posts with irrelevancies. It is that that makes them incomprehensible, to the point that I don't want to waste my time deciphering them. Relevant part of your paragraph (about 60-70 characters) : ~

when there is {}, ..., then there are sets... (Limberg)

Yes, there are sets (by your definition), perhaps even a theory of something if you formalize it, but there is no provably consistent set theory in the sense of our discussion. Set theories are powerful enough to include, at the very least, number theory. These can't be proved being consistent using any provably consistent theory (unless they are inconsistent). YohanN7 (talk) 12:13, 7 May 2014 (UTC)

You just don't get it!!! In ZFC there is the possibility that you get a statement "x∈M" and a statement "x∉M". So you would have a contradiction. With the Limberg-definition this is not possible cause sets have to be well-defined! So what I assume is that Gödels theorem is just not apllicable here. I don't see a way how you could possibly create a contradiction. Would it be about a statement of the form "x∈M" (so the contradiction would be "x∈M and x∉M"), a statement of the form "M is a set" or a "general" statement like "2+2=4"? I don't see any other possibilities. 93.197.19.94 (talk) 04:02, 7 May 2014 (UTC) Thomas Limberg (Schmogrow)

Again (see above), there are sets, but no set theory because Gödel says no. YohanN7 (talk) 12:13, 7 May 2014 (UTC)

I think it's a misunderstanding in the word "from" from your assertion "If the claim that it is consistent is provably true from your Limberg-definition, then, yes, 1 = 0 as well as 1 ≠ 0 will follow.". I thought it suffices to show at my definition that it would be consistent. But I think, you mean, it would actually be made use of the definition to show, it was consistent. Well, in that case, of course, it's possible that one can show an inconsistency. But that would be a beginners mistake. I didn't take that into account, therefore. Of course, one is not allowed to make use of a definition which's consistency he/she wants to prove! That is clear! OMG! See that's the problem, you live in a small world, where you were smart and others were dumb. And then you get a shock when reality proves you wrong! You shouldn't think I was stupid! When I talked about proving the consistency of my definition, I didn't make use of the definition. 93.197.19.94 (talk) 06:46, 7 May 2014 (UTC) Thomas Limberg (Schmogrow)

When proving the consistency of your theory, you didn't make use of its definition? What exactly did you use? Magic? Yes, I will get a shock when you prove me wrong. YohanN7 (talk) 12:13, 7 May 2014 (UTC)

I think what you don't realize is "The second incompleteness theorem only shows that the consistency of certain theories cannot be proved from the axioms of those theories themselves. It does not show that the consistency cannot be proved from other (consistent) axioms. For example, the consistency of the Peano arithmetic can be proved in Zermelo–Fraenkel set theory (ZFC), or in theories of arithmetic augmented with transfinite induction, as in Gentzen's consistency proof." from the article about Gödels theorems. 93.197.19.94 (talk) 06:52, 7 May 2014 (UTC) Thomas Limberg (Schmogrow)

Yes, certainly. (I guess you just found that out by the way you present it.) Exactly which consistent theory are you going to use to prove the consistency of yours? ZFC, assuming it is consistent? YohanN7 (talk) 12:13, 7 May 2014 (UTC)

Fascinating though this conversation is, I don't see a question here that can be readily answered by contributors to the Reference Desk. Have you considered taking this discussion to one of your talk pages? RomanSpa (talk) 15:30, 5 May 2014 (UTC)

He did have a question. Why isn't it obvious that his version of set theory has none of the flaws of other versions of set theory (and why he can't put it into our articles, naming it after himself). YohanN7 (talk) 16:27, 5 May 2014 (UTC)

And, in all fairness, he was asked to take the discussion here from the article talk page. YohanN7 (talk) 16:36, 5 May 2014 (UTC)

"I don't see a question here that can be readily answered by contributors to the Reference Desk", yeah, because I've already answered all questions by myself, so all that's left is to undo the undos of my edits to the article. 93.197.8.254 (talk) 16:52, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

I'll try to answer your questions.

First, note that the article that you have been looking at is Naive set theory. That is, it is informal and intuitive. One "naive" intuition is that any collection of all objects satisfying a particular condition can be turned into a "set". It turns out (e.g. Russell's paradox) that this is not the case, which is why various axiomatic approaches have been developed: they try to avoid these paradoxes. Your definition of a "set" similarly attempts to avoid problems ("A set is a well-defined collection of objects. A collection C is well-defined means that the definition of C doesn't contain or lead to an inconsistency about C."). To the extent that your definition manages to do this, it is no longer "naive". Thus, any edits that you make to the article on Naive Set Theory are inappropriate, because they're in the wrong place.

Second, the approach that you seem to want to follow seems to me to lead naturally to the consideration of Proper classes. As you will see from our article on that subject, the idea that you are proposing has been around for a long time, and has been extensively examined by many brilliant minds. Attempting to append your name to what (although it may seem new to you) is actually a fairly well-established idea looks rather silly.

Third and finally, I think you may have fundamentally misunderstood the nature of Wikipedia. It is a matter of policy that we do not include original research in this project. The reasons for this have already been explained to you. The correct place for new ideas is in the appropriate technical journal. To the extent that your idea is not new, it is already covered in Wikipedia; to the extent that it is original, we do not include it.

RomanSpa (talk) 18:25, 5 May 2014 (UTC)

" Thus, any edits that you make to the article on Naive Set Theory are inappropriate, because they're in the wrong place.". I've already considered your thoughts. But the thing is, I've just added some things (which are not so relevant I would say) to the definition that already was in the article. The word "well-defined" which avoids the paradoxes you've spoken of already was in the definition. Otherwise I wouldn't have taken the "naive" away. When you wanna show, what a naive set theory is, you should leave off the word "well-defined" so that you can say, that the definition is ambigues (or something) and can lead to paradoxes, justifying it to be called naive.

"seems to me to lead naturally to the consideration of Proper classes", I don't think so. Show it!

"Third", I know it's not new. I want you to recognize that it is not naive. That is no original research. You have stated something wrong (when one can consider the little improvements irrelevant). And I want you to change it. 93.197.8.254 (talk) 18:55, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

You awake the impression that all general set theories are naive and thus to be discarded and only the constructive set theories with its formalized axioms are not naive. But that's not true. 93.197.8.254 (talk) 19:01, 5 May 2014 (UTC) Thomas Limberg (Schmogrow)

It's night now in Germany, see you tomorrow! — Preceding unsigned comment added by 93.197.8.254 (talk) 20:21, 5 May 2014 (UTC)