Talk:Infinity/Archive 4

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Violation of Net neutrality (Isha Upnishad- invocation mantra)

Nothing useful here.

There is much talk about net neutrality and how Wikipedia is the harbinger of it. It is not true. As is apparent in the case of inclusion of an ancient Indian text that indubitably talks about the concept, this idea is being suffocated by some biased editors, most probably of European origin. It is sad because Europe is a great continent and has some really big contributions to mankind. By being thus petty in attempting to suffocate contributions by other civilizations, in my understanding, we are just belittling the great works of our civilization. I posted the following: It is sometimes alleged that the concept of infinity first originated in the Indian civilization as one of the mantras of Brihadaranyaka Upanishad and Ishavasya Upanishad popularly known as Shanti Mantra, around 700 BCE. The mantra is given in Devanagri script below. ॐ पूर्णमदः पूर्णमिदम् पूर्णात् पूर्णमुदच्यते | पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते || which means: That is perfect. This is perfect. Perfect comes from perfect. Take perfect from perfect, the remainder is perfect. . The debate arises because of translation difficulties between English and other languages. Simply put, the base word 'poorna' means complete or perfect. A question arises: are the words complete or perfect and infinity synonyms. An indirect way to answer the question is to look at the concept of infinity rather than the meaning of the word poorna. Infinity - Infinity = Infinity. The second line of the sholok says exactly that. On the other hand Complete - complete = zero. Another interpretation of the word is full . However, again since full - full = zero, the meaning full also does not satisfy the second line. The only constant that can satisfy the identity quoted in the second line is infinty. The debate however is not conclusive because satisfaction of the identity does not imply that the writer of the sholok was expressing infinity indeed. References I tried to be as careful to cater to any bruised egos. (Please read my edit). Is there any doubt that such an Upnishad existed, I have cited the Wikipage and that page cites proper publications for the Upanishad. Are each of the Wikipedia pages stand alone entities? If we start providing all the citations, each page would become bulky and unwieldy? Use of Wikipages to distribute citations is a prevalent editing methodology. I also cited from the published book of Honorable second president of India. The section just above "Early Greek" is doing exactly the same thing. I am a researcher and have some publications to my credit. I have no pride in making this addition. I did not do it, how can I have pride? I am doing it because Wikipedia as a share knowledge source should have all relevant information about a topic. There are other attempts to make the same additions, which were similarly rebuffed by the biased editors, without giving specific problems. The edits were just reverted. Anyways, I am looking for suggestions on the following: In its present state what parts of my edits are unacceptable and why? What else need to be added to make the unacceptable parts acceptable? Please provide specific feedback, so that we can come to a consensus regarding this edit. Regards, Wilkn (talk) 16:14, 29 August 2017 (UTC) Please note that comments like "This idea is being suffocated by some biased editors, ,most probably of European origin. It is sad because Europe is a great continent and has some really big contributions to mankind. By being thus petty in attempting to suffocate contributions by other civilizations, in my understanding, we are just belittling the great works of our civilization." and "I tried to be as careful to cater to any bruised egos" are not welcome here, and might prove unhelpful for your purpose. You might consider striking them. - DVdm (talk) 16:22, 29 August 2017 (UTC) Thank you Sir, but my asserted purpose is not to get this addition approved. While I respect the great contribution of the editors of Wikipedia, including the ones that I criticize, I am also as resolute and convinced about existence of bias. I respect your possibly disagreement with me on that. However, can you deny it possibility. I see such bias everywhere in India, in US, in politics, in literature. We cannot even deny its existence in research. Bias is human nature. Possibly, we sometimes practice it without even realizing it ourselves. I want this post to serve twin purpose. Arrive at a consensus regarding the addition and also highlighting the bias for possible self check. These two issues are disjointed. If my addition is evaluated based on my other assertions, then actually it will testify to my assertion. Kindly disregard my assertion if you disagree with it or deny it in your response. Please advise about the merits of my addition, I added another citation.Wilkn (talk) 16:36, 29 August 2017 (UTC) You seem to be confused about what net neutrality means. From the article here, "Net neutrality is the principle that Internet service providers and governments regulating the Internet must treat all data on the Internet the same, not discriminating or charging differentially by user, content, website, platform, application, type of attached equipment, or mode of communication." But back to the main point, which I've already mentioned multiple times, you're making claims without sources to back them up. You're making personal speculations, adding a {{cn}} tag, and then speculating some more to try to make it sound somehow more official. In an old thread up the talk page, it was even pointed out that the translation as "infinite" wasn't standard. Simply put, you can't just add your own commentary on the subject; you need to find secondary sources which make these claims. And even then, it would appear that such a claim would probably have undue weight if not countered by the fact that it's the minority viewpoint. --Deacon Vorbis (talk) 17:01, 29 August 2017 (UTC) References Again - the same bias without any supported citations. I have provided authentic translation, but you are making blanket statement without any citations. Provide citations that poorna does not mean infinite. Provide citations that my citations are not accurate. You view point has greater value that the published books? Provide citations that it is a minority point of view. Sir - you are an editor, if I may, just an editor. You have no authority whatsoever to challenge published work. Can any constant other than infinity satisfy the identity stated in the sholok? Kindly be specific in your responses to the question asked rather than equivocating. You seem to be practicing, what you are charging me of. The questions again are: In its present state what parts of my edits are unacceptable and why? What else need to be added to make the unacceptable parts acceptable? Can any constant other than infinity satisfy the identity stated in the sholok? Please provide specific feedback, so that we can come to a consensus regarding this edit. Wilkn (talk) 17:21, 29 August 2017 (UTC) It must be obvious to you by now that no-one supports your edits, or your interpretation. There are two possibilities: (i) you're a lone genius, and we're all fools; (ii) you're wrong. Even if (i) is true, it won't help you, because as you see you're not convincing: what you've said so far is unconvincing, and it is clear that you have nothing else to say other than repetition. Perhaps you should get yourself a blog? William M. Connolley (talk) 19:32, 29 August 2017 (UTC)   (ec) Hi Wilkn. I'll try to answer your questions here. In the present state, the entire edit is unacceptable; there is no part of it that may remain. What needs to be added is reliable sources (note that this is a Wikipedia term of art; you can't just read it in its ordinary English meaning) that show that this interpretation is held by at least some nontrivial minority of commentators (see WP:FRINGE for how to handle views that are held by a small minority but are nevertheless "notable", another term of art). It's irrelevant whether "any constant other than infinity" can be read into this passage. You have to show, and give reliable sources that show, that your interpretation is held out in the real world. You can't publish your original research here (third term of art; you really need to follow the links to understand these). I think you ought to know that there is a bit of a history here. This is not the first time that editors have asserted anti-Indian bias. There was an editor who went by the handle User:Jagged 85, possibly the most damaging editor in Wikipedia history. He (I'm just going to say "he" though I don't know that he was male) had a nasty habit of adding sources, but blatantly misrepresenting what they said. By the time he was banned, he had tainted the reliability of I think thousands of articles, and cleaning them up was a huge job that I'm not sure has been completed yet. The alleged bias by the West against classical Indian mathematics was one of his hobby horses. You of course are not responsible for this, but you should be aware that there is a reason that people's alert systems go up when this topic is raised. --Trovatore (talk) 19:48, 29 August 2017 (UTC) My follow up question is why are the three sources that I cite not considered reliable sources? As per my reading they are indeed reliable sources. I am reproducing exactly verbatim from the quoted sources. I am not putting any of my views over there as alleged. I have included citations that say that the sholok talks about 'infinite' as that it is a universally held understanding, including by western scholars such as Yeat, W.B. Why is the section about Early Greek fine? I was not even able to find the references when I searched for them. Apeiron can mean infinity? And what are the WP:RS sources that attest that Zeno of Elna came up with the concept of infinity. Kindly, calm down your alert systems, we are too small of entities to be able to represent Indian and/or Western contributions. For example, India and some western nations already have a space crafts in Mars. Now if we try to block publishing about it on Wikipedia, I doubt if we can hide it. Trovatore, thank you for sharing the history, things are obviously more in perspective now. Wilkn (talk) 21:17, 29 August 2017 (UTC) It's not so much that the sources aren't reliable, but that they don't support what you want to add. Neither of the first two used the term "infinite" or "infinity" in the verse in question. The third didn't even seem to contain that verse at all (it's possible I found something different though). Moreover, you're starting off with classic weasel words: "It is sometimes alleged that ..." – who alleges? And "The debate arises because of ..." – what debate? who's involved? And you're adding your own commentary/interpretation: "A question arises ..."; "An indirect way to answer the question ..." Who's raising the question, and who's trying to answer it? And so on. And it's also not just that the sources aren't reliable, but that they don't offer commentary on the verses. Bare translations of 2700 year old text aren't helpful when trying to source these claims. And once again, you'd need sources that make these claims, not just sources from which you can add your own interpretations onto. And even then, since this seems to be a not-widely-held view, you'd probably want to find other sources that offer different perspectives, and present those as well. --Deacon Vorbis (talk) 21:41, 29 August 2017 (UTC) Thank you Deacon, Trovatore! I possibly see you point more clearly now. I added those "weasel words" because I was on the defensive because of blanket reverting of mine and other people's edits without giving any reason. (Please see response of Mr. Connlley above). I thought the editors do not want to add the edits because they are getting intimidated by such an early Indian contribution and their European antecedents rather than the merit of the contribution. I have modified my addition as follows: In the Indian civilization, one of the mantras of Brihadaranyaka Upanishad and Ishavasya Upanishad popularly known as Shanti Mantra, around 700 BCE talks about a parallel concept of 'perfect.' The mantra is given in Devanagri script and its English transliteration is below. ॐ पूर्णमदः पूर्णमिदम् पूर्णात् पूर्णमुदच्यते | पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते || Om poornamadah poornamidam poornaat poornamudachyate | Poornasya poornamaadaaya poornamevaavashishṣyate || which means: "That is perfect. This is perfect. Perfect comes from perfect. Take perfect from perfect, the remainder is perfect." . Here the root word, poorna = perfect. Another interpretation of the word, 'poorna' is full . The identity stated can only be satisfied by the mathematical constant of infinity or infinite because complete - complete or full - full = 0 and not complete or full. Only infinity - infinity = infinity. . References What do you think of it now? My question about the problems with Early Greek section still remain unanswered. (As a side note, we need to add the identities of infinity (infinity (+-x/) infinity = infinity to the article and reference indeterminacy here as well. for example infinity/infinity = 0, infinity and 1.) Thanks! Wilkn (talk) 22:24, 29 August 2017 (UTC) I'm not sure we're making a lot of progress here. You claimed above that Yeats supported the "infinity" interpretation, but that does not seem to be backed up by the citation given. Neither the word "infinite" nor the word "infinity" appears in The-Ten-Principal-Upanishads. --Trovatore (talk) 23:06, 29 August 2017 (UTC) Trovatore - progress can be made only if both sides are willing. As a native speaker of the language, poorna and infinity are synonyms. The problem here is how to convince the obvious to any native speaker to a group of non-native, possibly prejudiced audience.:-) Please address my latest questions. Thanks!Wilkn (talk) 23:28, 29 August 2017 (UTC) You are not a native speaker of a 2700 year old language; nobody is. Just because the word is used to mean infinity today does not mean it was used that way 2700 years ago. This was already explained to you in another comment (I believe it was on wcherowi's talk page, if I recall correctly). Moreover, the whole bit about trying to justify by looking for a "mathematical constant" appears to be your own interpretation, which you can't just add along with a {{cn}} tag. You still need a source there. And if you take that out, there's no more connection to the article here. Moremoreover, stop accusing people of bias and prejudice. Read WP:NPA. --Deacon Vorbis (talk) 23:46, 29 August 2017 (UTC) >You are not a native speaker of a 2700 year old language; nobody is. Is this not a personal attack and an unsubstantiated allegation? Please see Sanskrit for more details. >Just because the word is used to mean infinity today does not mean it was used that way 2700 years ago. I am producing the citations of today's work. The section just above, 'Early Greek' does exactly the same thing. > Moreover, the whole bit about trying to justify by looking for a "mathematical constant" appears to be your own interpretation, which you can't just add along with a {{cn}} tag. You still need a source there. Why not? Again the section just above and all through the article the tag {{cn}} is freely used. Why am I not allowed to use it? Thanks! Wilkn (talk) 23:58, 29 August 2017 (UTC) Please indent your talk page messages as outlined in wp:THREAD and wp:INDENT — See Help:Using talk pages. Thanks. Re your remark that "progress can be made only if both sides are willing". Progress can only be made if you provide reliable sources for your final analysis: "The identity stated can only be satisfied by the mathematical constant of infinity or infinite because complete - complete or full - full = 0 and not complete or full. Only infinity - infinity = infinity." Two remarks about this: (1) this is a schoolbook example of our policy regarding wp:SYNTHESIS (in the Wikipedia sense of the word), and (2) why are you not allowed to use the {{cn}} tag? Because you need to provide the source, as opposed to ask others to do the work of finding support for your analysis, as explained in our policy wp:BURDEN. - DVdm (talk) 06:44, 30 August 2017 (UTC) Note: see Wilkn's Wikipedia:Requests for mediation/Does the invocation sholok of Isha Upnishad talk about infinity? - DVdm (talk) 14:59, 30 August 2017 (UTC) Side note on the rejected mediation Wilkn's attempt to invoke mediation appears to have been limited to the narrowest possible issue, namely whether a particular word in the Upanishads should be translated as "infinity". In point of fact, it is not difficult to find translations that render it as "infinity". The Yeats one, in particular, does not, and the fact that Wilkn claimed specifically that Yeats did interpret the Upanishads as referring to infinity may — bring back bad memories. But this is not really the point. It is entirely beyond my competence to render an opinion on whether the word is correctly translated as "infinity" in those translations that do so. Let's suppose for the sake of argument that it is. That still doesn't justify the text that Wilkn wants to add. Supposing the text is referring to infinity, it still doesn't seem to say anything substantial about it. (Wilkn appears to think that ∞−∞ = ∞ is a valid mathematical equation, but it is not; in any context I can think of, ∞−∞ is undefined.) If it can be established that the word is correctly translated as "infinity", then I might be persuaded that this is worth a single sentence in the text, as a very early example in which the concept of infinity is attested. Any more substantial mention, especially any claim that the concept "originated" (or even is "alleged to have originated") with the Upanishads, would demand citations speaking to that particular point. --Trovatore (talk) 20:07, 30 August 2017 (UTC) (Wilkn appears to think that ∞−∞ = ∞ is a valid mathematical equation, but it is not; in any context I can think of, ∞−∞ is undefined.) Trovatore - what does undefined mean? First technically, it is not undefined, it is called indeterminate. Moving forward arguendo. The equation called indeterminate because it has more than one answers: ∞−∞ = ∞ ∞−∞ = 0; ∞−∞ = -∞ As such - ∞−∞ = ∞ is a perfectly valid mathematical equation. Just that it is indeterminate or have more than one expressions. Each of the expression is a perfectly valid mathematical equation. So when some says x - x = x, the only, I emphasize only mathematical constant that can satisfy this expression is ∞. Similar to if say in a text written 100000 years ago, it was written x - 45 = 1. This means, according to present mathematics that was used to go to Mars or Jupiter or even outer space and which is used to make pacemakers, x = 46. As a side note, thanks to discussion, I came across another very peaceful set of mantras. I invite the rest of you to have a listen and read about it. Thank you so much for this enriching discussion. \url{greenmesg.org/mantras_slokas/brahman-nirvana_shatakam.php} In a synopsis - 1. I agree that having the word poorna translated to infinity is a valid demand. 2. However, since we are talking mathematics, the only constant that can satisfy the equation that is referred to in the second part of the sholok is infinity. This is a very strong support, if not it makes the conclusion absolutely indubitable. Please comment! Wilkn (talk) 20:28, 30 August 2017 (UTC) No, Wilkn, I'm sorry, you are quite wrong. ∞−∞ = ∞ is not a valid mathematical equation. ∞−∞ is undefined. --Trovatore (talk) 20:29, 30 August 2017 (UTC) If I am wrong then counter my supporting arguments. Please look up indeterminat and limits. You are challenging basic high school mathematics! Wilkn (talk) 20:32, 30 August 2017 (UTC) Please see extended real number line. Also be aware of the transitive property of equality, from which, if your first two equations ∞−∞ = ∞ and ∞−∞ = 0 were accepted, it would follow that ∞ = 0. --Trovatore (talk) 20:37, 30 August 2017 (UTC) Also, y'know, 0 - 0 = 0. Writ Keeper ⚇♔ 20:38, 30 August 2017 (UTC) Yep, probably about time someone pointed that out. --Trovatore (talk) 20:41, 30 August 2017 (UTC) I would reiterate that in Mathematics there is something known as indeterminate forms. Please see Indeterminate form. Indeterminate means it cannot be determined; it does <bold>not</bold> mean that it is undefined. A form is called indeterminate when we have more than one possible answers. Say for example ∞/∞ is an indeterminate quantity because anyContant/anyConstant = 1, but anyConstant/∞ = 0 and ∞/anyConstant = ∞. So for the form ∞/∞ there are three possible answers ∞, 0 and 1. Similarly ∞ - ∞ form has more than one answers, therefore, it is indeterminate. A simple google search may give you more information since this is a common topic in 8 and 9 standards across the world in calculus 1. It is widely used in determination of limits. Now how does that feed into our original discussion. If somebody asks what is x in the equation x - 45 = 1. The answer is x = 46. Now if somebody asks what is &infin/&infin. Our answer obviously is indeterminate. However, if someone says x/x = x, then the possible values of x are &infin, 1 and zero. Similarly, if someone asks ∞ - ∞ = ?, the answer again is indeterminate, but if someone says x - x = x, the only possible solution to this is x = ∞. Therefore, as per the translation of the sholok by acceptable Wikipedia citations the only constant that can satisfy the identity given in the second part is ∞Wilkn (talk) 04:17, 31 August 2017 (UTC) No, I'm sorry, you don't understand this topic. It is true that there is an indeterminate form called ∞−∞. What that means is that this is one of a closed-end list of seven "forms" that warn beginning calculus students that, if you're taking a limit of an expression, you have to watch out. If f(x) and g(x) both go to ∞ as x goes to some value a, then if you want to evaluate the limit as x goes to a of f(x)−g(x) as x goes to a, you see that the expression is of the "form" ∞−∞, so you know that you can't just "plug in the value a" to find the limit. You have to do something else. As a side note, "indeterminate forms" are still a useful pedagogical tool, but that's about as far as they go — they are not referred to in serious mathematics. It does not follow that the expression ∞−∞, intended as the result of subtracting ∞ from ∞, "can be anything". No. It's undefined, period. You cannot subtract ∞ from ∞. --Trovatore (talk) 04:26, 31 August 2017 (UTC) :-) You started with that it is indeterminate then you end up with it is undefined! Is is undefined or indeterminate? Wilkn (talk) 04:31, 31 August 2017 (UTC) No, I did not. I won't continue this point further here. Ping me on my talk page if you want me to explain. --Trovatore (talk) 04:36, 31 August 2017 (UTC) In truth, though, we've gotten off track here. I succumbed to the temptation to argue the point about indeterminate forms, because it's mildly interesting and brings up some common misconceptions. But it's entirely beside the point of this discussion. The fact is, as I said, there are available translations that use the word "infinity", and these could easily be cited. I am not in a position to argue with the translation. However the text is clearly not talking about mathematical infinity, or indeed mathematics at all — it's spiritual poetry, not math. This article is not strictly limited to mathematical infinity (though that's its main focus), so a brief mention of the Upanishads as an early attestation of the concept might be OK. But a brief mention, and certainly without any nonsense about ∞−∞ being ∞. --Trovatore (talk) 04:36, 31 August 2017 (UTC) I agree we got digressed. What do you think about the version below. I removed the mathematical conclusion: In the Indian civilization, one of the mantras of Brihadaranyaka Upanishad and Ishavasya Upanishad popularly known as Shanti Mantra, around 700 BCE talks about a parallel concept of 'perfect.' The mantra is given in Devanagri script and its English transliteration is below. ॐ पूर्णमदः पूर्णमिदम् पूर्णात् पूर्णमुदच्यते | पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते || Om poornamadah poornamidam poornaat poornamudachyate | Poornasya poornamaadaaya poornamevaavashishṣyate || which means: "That is perfect. This is perfect. Perfect comes from perfect. Take perfect from perfect, the remainder is perfect." . Here the root word, poorna = perfect. Another interpretation of the word, 'poorna' is full . Wilkn (talk) 04:47, 31 August 2017 (UTC) References Too long, and not clear to the reader what it has to do with infinity. Ideal would be if you could find secondary commentary, in a reliable source, mentioning that the Upanishads attest the idea of infinity. Don't try to include the original language; it may for all I know be very beautiful and worthwhile, but it's not appropriate in an article in English on infinity. A link to Wikisource would be OK though, probably in a footnote. And please keep it brief. The connection to the topic of the article is tenuous, so a sentence is probably enough. --Trovatore (talk) 05:11, 31 August 2017 (UTC) Not only is this proposed text about perfection too long, it is just totally off-topic in this article. It might be on-topic in article Perfection, but not here. - DVdm (talk) 06:00, 31 August 2017 (UTC) As far as I am concerned, I doubt if I can be more brief and do scientific justice to rationality. I see and understand your good faith concerns from a lay man's point of view and appreciate the concession that you are willing to make in spite of the fact that you see just a 'tenuous' relationship, but that does not negate my understanding of the 'truth.' For me, what you call is nonsense is basic math. I am not sure about your credentials and I never wanted to invoke it, but as a doctorate in Aerospace Engineering from one of the worlds renowned universities with several archival publications, I may have a little bit more understanding of basic math. Anyways, as I said I see and understand your concern. Kindly make it convenient to come up with a version yourself as per your point of view and we can review it? Wilkn (talk) 13:21, 31 August 2017 (UTC) Wilkn, of course it is not supposed to matter, but as long as you brought up the point first — I hold a doctorate in pure mathematics. --Trovatore (talk) 18:09, 31 August 2017 (UTC) Our personal understandings of the 'truth' and our credentials are of no importance in Wikipedia. You might read the essays wp:Verifiability, not truth and wp:Credentials are irrelevant. We need wp:Reliable sources and wp:CONSENSUS. The burden is yours—again, do read the policy wp:BURDEN. - DVdm (talk) 13:36, 31 August 2017 (UTC) As per my understanding, that is exactly what is happening here: you are using your credentials within Wikipedia and your group to suffocate the 'truth,' as I see it. The topic has come up again and again (please see the talk page above). If one topic that jumps out it is this one. Yours and Trovatore's opinion about it has also been far from constant. As far as I am concerned, I am citing reliable sources. According to me you are incorrectly citing the policies against me when they should be cited against you. At this juncture, the version I have above along with the mention to the statement that the only constant that can satisfy the identity of the second line is infinity. I can possibly come up with a citation from a high school math book to substantiate the identity. That is the best I can come up with. I am saying that with utmost sincerity. I also understand your 'genuine' concerns. At this point, I doubt if you and Trovatore are biased, that is why I suggested that you come up with a version and we can discuss it. At least we will have something to start with? Wilkn (talk) 13:52, 31 August 2017 (UTC) There are a few problems. Your statement that "the only constant that can satisfy the identity of the second line is infinity" is not itself coming from a reliable source. You are making that statement, you're not repeating that statement from a reliable source, and that's why it's inappropriate for Wikipedia; that makes it what we call synthesis, a type of (disallowed) original research. The second problem is that your statement that "the only constant that can satisfy the identity of the second line is infinity" isn't just original research, it's also wrong. Zero is also a value of x for which x - x = x is true; 0 minus 0 still equals 0. Finally, you are implying another statement: "since infinity is the only constant that can satisfy the identity, the mantra is talking about infinity". But this is also original research on your part--it comes from no source--and it is itself a tenuous statement; you're inferring the intent and the meaning of the mantra from mathematical principles that did not exist when the mantra was created. That we can rationalize the statement with our modern conception of infinity today doesn't mean that the mantra had to do with a concept of infinity at the time, and if it wasn't about infinity at the time, it's not relevant to the article. Regardless, these leaps to conclusions are precisely what we need reliable sources to explicitly support; our own reasoning is not sufficient for Wikipedia's purposes. Writ Keeper ⚇♔ 14:31, 31 August 2017 (UTC) All your three points are valid Writ Keeper and very well enunciated as well. Please see my response below. Point 1: I think it will be an overkill because in my limited understanding the identity is elementary, but I will try to find a citation from some high school book for the purpose? Point 2: You are right that I was wrong in saying that the only constant that satisfies the identity is infinity. However, there is something known as trivial solution in mathematics and we neglect it. 0 is a trivial solution. The last thing the word poorna can literally mean is zero! (Also, according to me what you just brought up is a relationship between infinity and 0. Your very simple statement is beyond my comprehension and is actually bigger than the universe itself. Sorry, for the hyperbole, but that is what it is. Everything originated from zero so possibly there is a relation between infinity and zero. I stop here because this is beyond my mental ability. :-). However, and although I doubt if I will find any supporters, I with all the force at my command (which I doubt I have any :-) ) will like your statement to be included in the final addition, if there is one.) Point 3: hmm the way logic works is that there are facts and we arrive at conclusions based on fact. There can be no citations for conclusions. Conclusions can be discussed and argued upon based on additional facts, but you cannot cite conclusions. Does Wikipedia not allow conclusions. Is it just a repository of facts? I do not see that, but could you please give a citation that is indeed the case as per policies? Wilkn (talk) 14:58, 31 August 2017 (UTC) Yes, Wikipedia is just a repository of facts; that's exactly what Wikipedia is. Wikipedia does not allow conclusions. This is enshrined in the verifiability policy: In Wikipedia, verifiability means that other people using the encyclopedia can check that the information comes from a reliable source. Wikipedia does not publish original research. Its content is determined by previously published information rather than the beliefs or experiences of its editors. Even if you're sure something is true, it must be verifiable before you can add it. It's also reflected in the already-cited no original research policy: Wikipedia articles must not contain original research. The phrase "original research" (OR) is used on Wikipedia to refer to material—such as facts, allegations, and ideas—for which no reliable, published sources exist. This includes any analysis or synthesis of published material that serves to reach or imply a conclusion not stated by the sources. [emphasis mine] So, in order to include this information, you would need a source that directly supports your conclusions. You would need a source that explicitly says "the Shanti Mantra talks about infinity". If your source doesn't explicitly discuss this mantra as talking about infinity, what you've done is synthesized material from separate sources to reach a conclusion not directly supported by either source--which is original research, and not allowed at Wikipedia. Writ Keeper ⚇♔ 15:08, 31 August 2017 (UTC) Point well taken. Thanks! So essentially you need a reliable source that says that the Shanti mantra indeed talks about 'infinity?' I know you already said that above, but just confirming. I will try to work on it and come up with such a source. Now back to some other things that need my urgent attention. Thanks all for a very enriching discussion and my apologies for any harshness on my part. I will be back with the source. — Preceding unsigned comment added by Wilkn (talk • contribs) 15:22, 31 August 2017 (UTC) How does this source look? It is a book, I am giving link to its web version. Please see the page 39: http://holybooks.lichtenbergpress.netdna-cdn.com/wp-content/uploads/Isopanishad.pdf Wilkn (talk) 15:39, 31 August 2017 (UTC) Umm. If I may ask, how come the single page containing the translation favoured by you (page 30 overleaf) is also the single page in the scan that appears to have been subsequently added to the original text? --Elmidae (talk · contribs) 19:18, 2 September 2017 (UTC) Of course! May I know what are you suggesting? :-) Perhaps you should buy the original book. The publisher information is there. If you think I will go to the extent of asking a publisher to change all copies of a book published in 1958 to suit my Wikipedia addition and the editor will comply, I can only commend you for your imagination. :-) I am seeing a new facet of Wikipedia and I am throughly enjoying it. One that attempts to hide truth because of personal biases and prejudices. I am a mere spectator here. Truth can defend itself. I am just doing my moral and ethical duty. Thank you pal, you made my day! :-)) Wilkn (talk) 00:44, 3 September 2017 (UTC) Leaving all that blustering aside, doesn't it strike you as strange that there's one clearly inserted page in the scan - not only in a different type and badly reproduced, but actually as a supernumerary page (there are now two pages between 30 and 32)? That doesn't say "reliable reproduction" to me... --Elmidae (talk · contribs) 01:09, 3 September 2017 (UTC) It agree with your fact, but not with either your premise of conclusion. What strikes me as more strange is that so many editors, who no doubt intellectual and well read, are ganging up to prevent an addition that shows ancient India in good light. It highlights the imperfectness of our existence. Honestly, I do respect Trovatore, DVdm, and Writ Keeper, but I am throughly surprised at their human infirmity. :-) Anyways! — Preceding unsigned comment added by Wilkn (talk • contribs) 01:24, 3 September 2017 (UTC) By golly, you have found us out! We do indeed hate everything India-related, don't hold with all that concept-of-zero and decimal system Eastern bullshit, believe Srinivasa Ramanujan was a fluke who lucked into a sinecure, and in general would like the subcontinent to just quietly slink off and stop embarassing us. - Might I suggest you find another focus of argumentation? This one is not going to win any arguments. --Elmidae (talk · contribs) 02:06, 3 September 2017 (UTC) Perhaps we should concentrate on the topic at hand. If you have any other valid questions to the addition, please ask. Rhetoric can only carry you that far. Wilkn (talk) 02:13, 3 September 2017 (UTC) Excellent notion. So, what are your thoughts on the reliability of that apparently post-factum copied-in page in your source? If I saw something like that in a scan, I'd assume it had been tampered with and was not part of the original document. --Elmidae (talk · contribs) 02:53, 3 September 2017 (UTC) ha ha! "tampered with, post-factum copied in page in *your* source!!" Oh my God!! Why do you think somebody tampered with this book "post-factum?" May I please have you give full vent to your conspiracy theory before I attempt to help? Sir - it is written below it - That page is selected and Adapted from "Paul Brunton's spiritual crisis of man." Now we have two citations. I can see your doubt and also possibly, your skepticism, but your conclusions were quite refreshing. Anyways, so what next now? — Preceding unsigned comment added by Wilkn (talk • contribs) 06:45, 3 September 2017 (UTC) (insert) In a last attempt to bring the concept of "reliable source" across. Wilkn, here is an electronic full-text of Paul Brunton's "The spiritual crisis of man". It does not contain the "cited" passage, or anything like it. So now we are two layers deep into doubtful sourcing. If you can't produce anything better than that, you are not making a convincing case. Can we please put this to rest now? --Elmidae (talk · contribs) 19:21, 4 September 2017 (UTC) Nothing next: no one is sympathetic to your attempts and there is clear consensus against every edit you have proposed. You should find some other way to occupy yourself. --JBL (talk) 12:32, 3 September 2017 (UTC) I don't see any clear consensus. There have been few participants in this discussion and none of them have been able to properly counter that the edit should not be there. I defy you to give a single valid reason to not have the edit, other than blatant personal prejudice and bias and low self esteem. Shameful conduct! Do you want to have a vote with each participant voicing a yes or a no along with their reason thereof? (Thanks for teaching me outdent, I have no reason to stop, particularly when I am on the side of truth. Obviously, such blatant bias and prejudice need to be exposed. Some of the participants are well respected scientists and researchers, such unequivocal suffocation of truth will enhance their reputation tremendously.) Wilkn (talk) 17:34, 3 September 2017 (UTC) Elmidae Pasting from Tarage's talk. Thanks for your investigation of Paul Brunton's book! I will look it up myself and let you know where if anywhere the cited text appears. Wilkn (talk) 00:28, 5 September 2017 (UTC) Elmidae and rest, I will need sometime, but I will get back about if I can find the quoted text in the Paul Brunton's book. I will also investigate further, if my alleged interpretation of translation is found in any other sources. I realize it fully well that it is my ethical duty to inform you of my failure as much as it is to inform you of my success. Thanks for this very enriching discussion! Wilkn (talk) 04:39, 5 September 2017 (UTC) Elmidae Hi Elmidae, the following two citations give the meaning described above: The Upanishads, Part 2 (SBE15), by Max Müller, [1879]. Page 189 and Credits English translation of Brihadaranyaka Upanishad by Swami Nikhilananda. page 61. Also, please see wikipedia page Shanti Mantrafor more translation references. Let me know if you have any other follow up questions. Wilkn (talk) 03:56, 11 September 2017 (UTC) While I cannot check these, I'd say (AGF) that this likely represents two or three usable references, and would assume that the specific issue from above (provided source not containing claimed statement) should be addressed thereby. As to the general advisability of including the information in the article, I will not enter the discussion and would like to leave that assessment to the previous discussion participants. --Elmidae (talk · contribs) 04:36, 11 September 2017 (UTC) Thank you for your agreement to the validity of the citations Elmidae! I have been banned from making edits. May I have you or other participants of the discussion DVdm, Writ_Keeper, Trovatore or anybody else to make the addition to the page? Wilkn (talk) 19:02, 11 September 2017 (UTC) I would like to point out that your ban extends to this talk page (on this subject) and you have hereby already violated the terms of that ban. It is clear from your latest comment why the ban was put in place. Elmidae did not agree to the validity of your citations and stated that they were not viewed. It was only by assuming good faith on your part that these citations looked like they might be valid. However, the same can be said of any number of previous "citations" that you have provided that turned out not to say what you claimed they said. --Bill Cherowitzo (talk) 19:41, 11 September 2017 (UTC) So now what you will put me on the electric chair! :-) I am not sure, if your realize this or not, but an unfair ban on me does not bother me, then whether it is for the whole of Wikipedia or just this page. I did nothing to deserve the ban. I have tried my best to address the questions and reservations of everybody, in spite of gravest provocation and lowly behavior in a reasonable way. Regarding your allegation, which of my citations did not say exactly what I quoted them to say? The only question was the credibility of the citations rather than what I said about the citations. Kindly, go an make the change on the page if you also find the citations to be credible, feel free to verify the citations as well and let me know if you have any other reservations. Wilkn (talk) 19:52, 11 September 2017 (UTC) Go away. --JBL (talk) 20:11, 11 September 2017 (UTC)

links

@Deacon Vorbis:

how any of these links are an actual problem to the any reader...

Why it is there is an article titled concept since it is such an ordinary word, if your understanding were true, no-one would need to read the article, since the topic is such an ordinary fact of life 23h112e (talk) 21:04, 26 November 2017 (UTC)

Why your opinion should supercede my own in any case, while you state policy, although how, since there is the possibility of error on your account, as indicated by ther confusion on your part between ordinary and everyday, and the non-absolute description in policy of behaviours with respect to under and overlinking, a factor to which I refer to due to you so helpfully including mention in your editorial summary. 23h112e (talk) 21:13, 26 November 2017 (UTC) 23h112e (talk) 21:14, 26 November 2017 (UTC)

Side note: you don't need to ping me every time you write here; I'm watching this talk page. "Ordinary" and "everyday" are synonyms here. You seem to have difficulty with English; I don't mean this in a disparaging way at all; I'd be pretty hard-pressed to communicate in any language other than English, myself. But your confusion over "everyday" versus "ordinary" is a problem here. It's also difficult to follow what you're trying to say. While I think I get the overall gist of what you're saying, it's hard to be sure exactly what you mean, because the English you're using is so awkward (I've had the same problem with many other comments you've written, too). One possibility is to try editing the Wikipedia of whatever your native language is; it could probably use some help too, and you may be more successful when you need to communicate with others.

But back to the overlinking, "abstract" and "concept" are ordinary, everyday words. It's especially important in the opening sentence not to link to things that aren't really directly related because such links are just a distraction. –Deacon Vorbis (carbon • videos) 23:22, 26 November 2017 (UTC)

introduction - "larger than any number"

for example:

any number, the largest number is... (there isn't one) obviously, there is no largest number - unless it is a counted number of actual things, anything obviously.

To re-iterate, the largest number actually of any concrete thing is perhaps the number of atoms in the observable universe (which is uncountable in any case, since no-one knows the entire universe), the number of stars in the observable universe - which is presumably a number which might be in the future known; or might already be known - is a number; +1 of this second number does not equal infinity.

Anything which is an actual observable thing, which has any relationship to infinity since infinity by definition - is never reached, is not graspable, is not an actual number, (to re-iterate again) since any number stated is therefore having +1 as a larger number (or +0.00000...n...>1).

Numbers refer to actual things, for those things to have number applied to them, to be counted, even if it is a non-known number, for example - atoms in the universe, there is still the +1 factor which therefore denies the infinity to the number.

"without bound" is obviously the actual correct definition, because, if it were possible to imagine any situation where infinity might occur in the universe, it is simply a matter of lack of knowledge of the actual number of the things, which allows the incorrect presumption of infinitesimal. Every thing in the universe has number, without bound suggest the theoretical travelling in any direction from earth, to the boundaries of the universe > [1], and the thing which is beyond - this is the true and only actual referent to infinity, infinity is ipso facto this definition and this does not include the "larger than any number" definition.

23h112e (talk) 22:02, 19 November 2017 (UTC)

@Deacon Vorbis: 23h112e (talk) 22:06, 19 November 2017 (UTC)

https://en.wikipedia.org/w/index.php?title=Infinity&action=history:

• 20:55, 19 November 2017
• 20:52, 19 November 2017‎
• 20:02, 19 November 2017
• 18:49, 19 November 2017‎

23h112e (talk) 22:11, 19 November 2017 (UTC)

Your comment is kind of a jumbled mess; I'm not really sure how to respond to it, but I'll make a few points anyway. In terms of numbers, the ordinal number ω is in fact larger than any integer, so it depends on what number systems we're talking about. This is the lead of the article – an article that's about a vague, abstract concept. A certain amount of latitude is understandable in trying to discuss it. Moreover, the article lead isn't (just) for defining the subject of the article; it's for summarizing the key points in the rest of the article. Moremoreover, things (infinity included) don't always have a single description or definition; they can have many. And as for "numbers refer to actual things" – they might, but they might also refer to fake things, or to no things at all. I'm really at a loss as to your objection here.

Side note, I also don't know why you posted a bare URL of the article history along with some dates. --Deacon Vorbis (talk) 22:27, 19 November 2017 (UTC)

Well, 23h112e does make at least one useful point here. We're deliberately vague on whether infinity is a "number" (see lots of discussions in the talk history). But if infinity is in fact a number, then it can't be larger than "any number", because it isn't larger than itself.

I will change this bit to "larger than any natural number", as a stopgap. That is actually one of the definitions of infinite quantity. I'm not trying to shut off discussion; there could be better solutions. --Trovatore (talk) 23:46, 19 November 2017 (UTC)

---

---

@Deacon Vorbis: @Trovatore:

try imagine https://en.wikipedia.org/wiki/%CA%BBOumuamua as it appears in the moving image here, if it were to continue, then it would eventually cease due to lack of energy, or impact, although to then project a course in the direction shown, since the universe cannot have a boundary, it would (in the imagined situation; circumstances) continue forever in the direction "without bound" suggest the theoretical travelling in any direction from earth, to the boundaries of the universe as shown at 22:02, 19 November 2017 (UTC) 23h112e (talk) 18:24, 21 November 2017 (UTC)

I utterly fail to see your point. What does all that have to do with the price of tea in China? --Deacon Vorbis (talk) 01:28, 22 November 2017 (UTC)

@Deacon Vorbis:

actually the price of tea in China currently (a cake of two-year-old Ye Sheng Gucha tea costs 260 yuan (about £18) is about a million miles away, or more, from the focus of the current discussion - tell me where your mind is heading to, which direction of thought were you intending to take me in ? (and I don't eat cake in any case, by the way) 23h112e (talk) 17:13, 23 November 2017 (UTC)

Extraordinary 23h112e (talk) 17:17, 23 November 2017 (UTC)

Please indent your messages when replying to someone; see Help:Talk for more detail. Also, pinging doesn't work unless you sign your post when you use it. As for the tea thing; see wikt:price of tea in China for a definition. The point was that nothing you said in your previous post seemed to have any relevance to anything about the article here. --Deacon Vorbis (talk) 17:31, 23 November 2017 (UTC)

@Deacon Vorbis: c.f. (ignoring the links to youtube) - https://en.wikipedia.org/wiki/User:23h112e/sandbox#26th 23h112e (talk) 21:06, 26 November 2017 (UTC) hoping this is sufficiently elucidative for you, considering your apparent doubting of my actual abilities to grasp something, although sitting here I'm sure I see and understand something you haven't quite completely grasped about me, to allow you to be so free as to pass comment on anything about me with certainty 23h112e (talk) 21:17, 26 November 2017 (UTC)

I'm thinking because i'm actually correctly describing uncountable, and you have found me to do so, you therefore have concluded I am defined as an individual also uncountable, which therefore some-how empowers you to negate my contributions by your own subjective logic. 23h112e (talk) 21:20, 26 November 2017 (UTC)

No, your link isn't specific, and it doesn't help me understand your point. I still don't understand what you're trying to say. Nothing about the astronomical body had anything to do with the article or what you had tried to remove from it. –Deacon Vorbis (carbon • videos) 23:26, 26 November 2017 (UTC)

@Deacon Vorbis: hello from here Deacon (not philosophy instead) - "The layman often perceives it as a kind of "number" larger than all numbers..." Princeton University Press, 1991 Eli Maor is a teacher of the history of mathematics who has successfully popularized his subject with the general public

original search page, criteria is "ancient Chinese infinity philosophy" text - p.2 I'd like to know your opinion on the statement by Eli Maor (additionally considering is a teacher of the history of mathematics (doesn't mention professor)) 23h112e (talk) 16:54, 19 December 2017 (UTC)

Yes, it's a statement (which loses some meaning when taken out of context). What about it are you asking my opinion of exactly? –Deacon Vorbis (carbon • videos) 17:10, 19 December 2017 (UTC)

Hindi

In hindi, we call it anant not ananta. And it is the problem that in English, they include "a" at the end. अनंत is the spelling and we read it as anant.
117.207.26.105 (talk) 20:11, 14 May 2015 (UTC)

I think "ananta" is appropriate to use in english as per rules of grammer Navjot1200 (talk) 16:19, 24 January 2018 (UTC)

∞

I think it is a concept rather than a Number as considered in Mathematics.... Navjot1200 (talk) 16:18, 24 January 2018 (UTC) Navjot1200 (talk) 16:18, 24 January 2018 (UTC)

The very first sentence of the article already calls it a concept. Later in the article, there's some discussion on various number systems that involve infinite quantities. There's also Infinity (philosophy) for less mathematical views on the subject. –Deacon Vorbis (carbon • videos) 16:25, 24 January 2018 (UTC)

Theology

I think an article on the Christian theological concept of infinity should be added. As the Catholic Encyclopedia states: "When we say that God is infinite, we mean that He is unlimited in every kind of perfection or that every conceivable perfection belongs to Him in the highest conceivable way. In a different sense we sometimes speak, for instance, of infinite time or space, meaning thereby time of such indefinite duration or space of such indefinite extension that we cannot assign any fixed limit to one or the other. Care should be taken not to confound these two essentially different meanings of the term." — Preceding unsigned comment added by 24.191.87.42 (talk) 00:19, 21 March 2012 (UTC)

• I'd be happy just to have some brainiac prove that infinity is more than a mathematical concept and has real-world application. In a world of quantum-mechanics, nothing can be measured to infinite degrees of certainty. Religious faith goes beyond what science can prove. I'm just being a realist. — Preceding unsigned comment added by 2600:6C48:7006:200:D84D:5A80:173:901D (talk) 03:38, 17 March 2018 (UTC)

Physics and Infinity

I could argue that most - if not all - aspects of Infinity in the area of Physical Sciences (Physics) are purely mathematical in basis. Infinity is a mathematical concept intended to represent very large numbers that are (at least thus far) immeasurable and cannot be determined to be finite. Pure physics relies on observations to confirm its theories, and yet all measurements contain experimental error and it is not possible to observe the entirety of infinity. Lack of citation on Physics-based applications of infinity only support my position. I invite others to add to this, or update the article accordingly. I'd prefer to remove reference to Physics from discussion of Infinity, but I think others need to contribute. --68.188.183.91 (talk) 02:30, 20 February 2015 (UTC)

You are making a philosophical argument here; it's not directly relevant to what should appear in the article. No doubt there are reliable sources that have made similar arguments, and those can certainly be cited. However, it is also true, for better or for worse, that the notion of infinity has been and continues to be used in physics, and we are not going to avoid mentioning that just because you don't think physics should use it. --Trovatore (talk) 08:14, 20 February 2015 (UTC)

The article "infinity" should not be purely a mathematical concept. There are great philisophical concepts. Consider death, for sample. You can't measure infinity, or any physical constant to infinite degrees of certainty. Throw in quantum mechanics - there is no certainty. You can't talk about infinity without uncertainty.--2600:6C48:7006:200:D84D:5A80:173:901D (talk) 03:28, 17 March 2018 (UTC)--2600:6C48:7006:200:D84D:5A80:173:901D (talk) 03:28, 17 March 2018 (UTC)

See Infinity (philosophy). Paul August ☎ 12:23, 17 March 2018 (UTC)

Large-scale LaTeX edits for consistency

@Joel B. Lewis: Per MOS:FORMULA that you cited, "[...] from non-LaTeX to LaTeX without a clear improvement," I believe there is a clear improvement and keeps consistency in the article (WP:ARTCON); LaTeX would be preferred over {{math}} as the symbols are clearer, in my opinion; in addition, "English Wikipedia currently has no consensus about preferred formatting," and "Large scale formatting changes to an article or group of articles are likely to be controversial," therefore I do not know how you can say it is discouraged when it explicitly states it is "likely to be controversial." {{u|waddie96}} {talk} 12:21, 30 October 2018 (UTC)

Your claim that one is clearly better is immediately contradicted by the fact that there is no consensus. The fact that you were reverted means that it was controversial. It is definitely not an improvement to use LaTeX for individual small inline formulas, given current viewing options. (Maybe at some point it will be -- that will be nice -- but it isn't now.) --JBL (talk) 13:31, 30 October 2018 (UTC)

@Joel B. Lewis: "It is definitely not an improvement" is your opinion. Contradicting your first statement that there is no consensus. Do you see the issue here? Please go through the article then and change all inline formulas to {{math}} instead of <math> to maintain consistency per your opinion. There needs to be either or Joel. {{u|waddie96}} {talk} 18:23, 30 October 2018 (UTC)

Joel B. Lewis is certainly not alone with this view. There are several experienced math editors (but certainly not all) who would agree with him, myself included. In-line LaTex, with its alignment, size and intensity issues can and does at times make the visual presentation awkward. There are times when its use can't be helped, but these are relatively rare. Wholesale LaTexification is really not a good option at this point in time, and certainly not without some consensus on the talk page for it.--Bill Cherowitzo (talk) 18:59, 30 October 2018 (UTC)

Mistake in diagram in "Cardinality of the continuum" section

In the "Cardinality of the continuum" section, the diagram displays the first three steps of a fractal to generate a space filling curve.

I think that the first step is wrong: it seems that the horizontal lines shouldn't be right at the top and bottom of the image, otherwise in the next steps the lines would overwrite each other. Instead, the horizontal lines should only be near the top and near the bottom.— Preceding unsigned comment added by Richierocks (talk • contribs) 08:07, 15 March 2015 (UTC)

"Mathematics uses the general concept of infinity"

This is a terrible phrase in the article. The "concept" has already been explained as a purely philosophical item. What is it supposed to mean that mathematics uses a philosophical concept? At best it explains nothing, except it creates confusion. The truth is that the infinity symbol ∞ is used in mathematics to abbreviate expressions involving limits, typically in summations and integrals. There is no "concept" involved, since you could freely choose to replace the symbol by the more tedious original limit expressions without changing the meaning. The symbol is also used in situations, in topology, elliptic curves, and real and complex analysis, etc., when it is practical or necessary to add an additional element to an existing structure to obtain a larger structure with desired properties. The "extra" element is traditionally named using the symbol ∞. There is no concept whatsoever involved in this choice. The statement "mathematics uses a concept of infinity" is a basic misunderstanding. — Preceding unsigned comment added by 90.185.71.194 (talk) 20:14, 17 February 2019 (UTC)

The substance of what you've written supports, rather than refutes, the (true) statement that the concept of infinity is used in mathematics in various different ways. Though of course your list of places where the concept is used is far from complete, and your interpretations of the various uses of the concept are idiosyncratic at best. --JBL (talk) 20:49, 17 February 2019 (UTC)

The concept of infinity was, until the end of 19th century, a purely philosophical concept. Now, it is also a mathematical concept, which is rather different from the philosophical one; for example, in mathematics, there are infinite sets of different size, and the possible sizes have been quantified and studied (see Transfinite number). So mathematics use a concept of infinity that is not exactly the philosophical concept. I have edited the lead of the article for clarifying that. D.Lazard (talk) 21:11, 17 February 2019 (UTC)

I have some concerns about the new wording, in particular the claim that In modern mathematics the concept of infinity has been formalized. For one thing, I think it puts too much emphasis on formalization. Also the reference to "the" concept of infinity sounds as though there is only one, when in fact there are different sorts (at least three: transfinite cardinals, transfinite ordinals, extended real and complex numbers, and a possible fourth with infinities from nonstandard models). (This would be less of a problem if we weren't talking about formalization.)

I am also not sure I agree with the rationale expressed by D.Lazard above. I would agree that the modern mathematical concept(s) of infinity is (are) rather different from the historical philosophical concept, which I suppose means more or less what Aquinas thought. But Cantor arguably initiated a new philosophical concept, which continues to this day. --Trovatore (talk) 21:52, 17 February 2019 (UTC)

One may argue infinitely about what is philosophy and what is not. This been said, there was clearly a need to clarify in the lead that, in mathematics, infinity has been made more than a concept, and is rather different from the intuition that anyone can have. I think that Trovatore and I can agree on that. The difficulty is to find a formulation (in one or two sentences as needed in the lead) that is not controversial. I think that my version is better than the previous one, but it is only a first draft that needs work for reaching a consensus. Specifically, I have hesitated between "the concept of infinity" and "a concept of infinity", and also between the words "formalized", "refined", "expanded", ..., all expressing a part of what Cantor and his followers have made to the concept. In any case, a better formulation than mine would be welcome. D.Lazard (talk) 09:38, 18 February 2019 (UTC)

I like "refined" a lot. --JBL (talk) 12:07, 18 February 2019 (UTC)

Infinity in mathematics

I have completely rewritten the part of the lead devoted to mathematics. IMO, this is simpler and much clearer for a large audience. I guess that discussing of further improvements would be easier with this version than with the previous ones.

In particular, the axiom of infinity must appear in this article, but I am not sure whether this should be in the lead or in the body. D.Lazard (talk) 15:10, 18 February 2019 (UTC)

I like it. I would not put any particular axiom in the lead, as it strikes me as too specific to a particular axiomatization. --Trovatore (talk) 02:11, 19 February 2019 (UTC)

Infinity as theory of blackness

I have posted this under Infinity in a section I created and titled "uses in african-american theory". It got deleted for some reason and I would really like to reach out and ask for help from the community. I hope I get pointers about why it was deleted and what I can change in order to repost it and keep it there. Thank you so much for all the efforts and a the help.

" the indeterminacy of infinity in Math has been extrapolated as a philosophical and critical signifier in African-American Studies, in order to situate racism and antiblackness as determinate values of Western thought that need the indeterminacy of blackness to be defined and sustainted. Denise Ferraira da Silva, Professor and Director of the Social Justice Institute at the University of British Columbia, theorizes on the value of blackness rendered obsolete. In her article entitled “1 (life) ÷ 0 (blackness) = ∞ − ∞ or ∞ / ∞: On Matter Beyond the Equation of Value”, da Silva uses numbers and equations towards her argument that blackness exists without value and without form. Here, the mathematical use of infinity is conceptualized as a discourse of “refusal to contain blackness in the dialectal form” . Equating blackness with infinity signifiers an impossible/indeterminate value that is not bound by categories and premises of modern thought." Ktf87 (talk) 18:32, 23 March 2019 (UTC)

@Ktf87: The reasons were given in edit summaries; you can click the "View History" tab at the top of the page to see the summaries that were used along with the various edits that removed the material you've been trying to add. Since there's already a discussion at Talk:Infinity (philosophy) (which would at least be a slightly better place for this sort of material) about the same topic, I'll keep any further discussion over there rather than here – I just wanted to draw your attention to the reason(s) used for removal, since you seemed unclear. –Deacon Vorbis (carbon • videos) 20:23, 23 March 2019 (UTC)

Finite, unbounded, and infinite.

It is pobably not Wikipedia's job to correct this. I'm guessing that primary mathematics publications must correct this error first, which I suspect will take some time.

The wikipedia definition confuses the terms unbounded (without any bound) and infinte (beyond counting). Mathematical inconsistency results from a lack of clear definitions of the terms finite, unbounded and infinite. Finite is unbounded which means that it can tend to infinity. In analysis we consider what would happen in the limit (i.e. if we could allow finite to become infinite). In algebra allowing unbounded to be infinite has always been illegal (prior to Cantor which I reject). Unbounded is best thought of as the never-ending journey from finite to infinite, it is not the same as infinite because the journey never gets there (except through analytic reasoning). Paraxoxes vanish once this is properly understood. See and . Epdarnell (talk) 12:56, 29 August 2019 (UTC)

References

It is pobably not Wikipedia's job to correct this. Indeed: see our policy WP:NOR. --JBL (talk) 13:12, 29 August 2019 (UTC)

Reference to God missing

Some reference to God (because e.g. Allah or Bible God is only solely considered Almighty) should be added to the article. Only infinity could make almightiness possible (e.g. drawing out energy to the infinite extent in order to have for the entity in question, God in this case, the ability to do whatever it/He wants).

Currently there is about 3.42 million (or 3.3m when archive.is performs search) results on "almightiness of God infinity" Google searh, so proper reliable sources can be found for sure. --5.43.99.155 (talk) 04:35, 26 September 2019 (UTC)

While WP can certainly not assert any of your points in its own voice, I actually do think there is a decent case to mention theological or otherwise spiritual aspects of the notion of infinity, and indeed they are mentioned at Absolute Infinite and at infinity (philosophy). The division of labor between infinity and infinity (philosophy) is a little unconvincing, and I wouldn't mind seeing them merged if it could be done well. As a side note, it's more than a bit odd that none of these articles mentions Aquinas. --Trovatore (talk) 05:20, 26 September 2019 (UTC)

Very large infinite sets

While "very large infinite sets" can be meaningful, it's also surprising to the naive reader, and is not really explained in situ. For that matter it might be confusing to the expert reader as well, who might assume that this means that the proof uses large cardinals, which (I'm not certain but) I think is not the case.

It seems likely that it probably means it uses the set of all sets of reals, or something smaller than that. That's a "very large infinite set" in some sense, but not in all senses. We should (i) figure out what the real situation is, and then (ii) figure out how to express it in accurate but understandable language. --Trovatore (talk) 02:55, 8 October 2019 (UTC)

@Trovatore: Real quick, just FYI, I also just posted a thread over at WT:WPM about this as well. –Deacon Vorbis (carbon • videos) 02:57, 8 October 2019 (UTC)

Looking at the history, it looks like the statement was added by D.Lazard in this edit. Maybe he'll want to weigh in. –Deacon Vorbis (carbon • videos) 03:05, 8 October 2019 (UTC)

@Trovatore: I mentioned it in the WPM discussion, but the proof uses Grothendieck universes so it is about the existence of certain large cardinals in ZFC. — MarkH21 (talk) 04:55, 8 October 2019 (UTC)

Hmm ... Grothendieck universes 'aven't got much large cardinals in 'em, but still, it's more than I was expecting. That's the kind of thing that's often eliminable by a minor reworking of the proof, but of course I don't know the proof, so it's hard to say in the specific case.

Not really sure where to go from here. "Very large infinite sets" is still surprising to the naive reader and possibly misleading to the expert reader (who might expect it to mean more than piddly little inaccessibles). But no good rewording immediately leaps to mind. We certainly don't want to get into Grothendieck universes (or large cardinals, for that matter) in the second paragraph of the general article on infinity.

I see that someone has linked the Grothendieck-universe article, which is something I guess, though in general I dislike hiding information in piped links. In principle links should be for convenience, not for information that belongs in the article (they don't appear in printed versions, for example). --Trovatore (talk) 05:39, 8 October 2019 (UTC)

Yes, I just added the reference and the piped link because it was immediately better than the previous state. I don't have any strong feeling for the current state though, so feel free to tweak or remove. — MarkH21 (talk) 06:03, 8 October 2019 (UTC)

Many thanks for these edits. I have added in the preceding sentence a phrase about the "size" of infinite sets, which may also help to understand "very large". Feel free to remove it, if you think it is too much detailed. Nevertheless, I think important to insist on aspects of mathematical infinity that are paradoxal for non-mathematicians. D.Lazard (talk) 09:04, 8 October 2019 (UTC)

Yep, thanks to all for taking a look at this one. –Deacon Vorbis (carbon • videos) 14:29, 8 October 2019 (UTC)

The qualifier "very large" is controversial, as this section abundantly illustrates. In context, it is also totally unnecessary. I am deleting these two words and the associated link. The reader does not need to understand what they mean. Peter Brown (talk) 19:15, 9 October 2019 (UTC)

I'm fairly ambivalent about this note being here at all, but saying it's due simply to the existence of infinite sets makes it plainly incorrect, so I've reverted the removal of "very large" once again. It also doesn't appear to be "controversial" so much as just needing explanation/context. –Deacon Vorbis (carbon • videos) 19:29, 9 October 2019 (UTC)

I agree with Deacon Vorbis in principle - it’s kind of meaningless to say that the proof depends on the existence of infinite sets. Most of mathematics does. Pedantic note: ... uses the existence of infinite sets is correct in the literal sense though... it depends on the infinitude of the natural numbers for instance. That’s a pretty meaningless example though as it’s nothing even remotely particular to FLT. — MarkH21 (talk) 19:41, 9 October 2019 (UTC)

(edit conflict) Nobody at all has suggested that "it's due simply to the existence of infinite sets" (your wording). It is necessary to claim only that the proof uses the existence of infinite sets, my preferred wording, which is true. Specifically, the proof uses the existence of Grothendieck sets, but that's a refinement that the user need not be troubled with. In such an elementary presentation, even linking to Grothendieck universe is probably overkill, though it is appropriate to get into the matter in sourcing the statement. What's relevant, here, is only that a proof in number theory uses some kind of set that is infinite. Peter Brown (talk) 20:42, 9 October 2019 (UTC)

The topic of the paragraph is "The mathematical concept of infinity is used everywhere in mathematics… ". Further discussion is necessary only because some readers are likely to think, "Hey, that can't be true of number theory." To fostall that reaction, the pargraph needs to add, "Yes, it's even true of some proofs in number theory, including a proof of Fermat's Last Theorem, which you may have heard of. Here's a relevant source." There is no need to go into any detail as the the kind of infinite entity involved. Peter Brown (talk) 20:33, 9 October 2019 (UTC)

Just on the point of number theory in general, I don’t think that’s very likely, nor is the fact that FLT uses some infinite set all that surprising. The very statement is about the integers which is an clearly infinite set. Even the most basic result, that there are infinitely many primes, is about infinitude and due to Euclid 2300 years ago. — MarkH21 (talk) 21:00, 9 October 2019 (UTC)

D.Lazard introduced into the article the idea that "number theory … may seem to have nothing to do with it [infinity]." I concur. It may seem so to some readers, and further discussion is needed to dissuade them. Peter Brown (talk) 22:40, 9 October 2019 (UTC)

IMO, it is important to insist that, in modern mathematics, infinite sets are manipulated as actual objects not as the result of a unbounded process. The concept of actual infinity is so common for mathematicians that many forget that it is paradoxal (or even ignored) for non-mathematicians, including many philosophers. A witness of this ignorance is the body of this article itself: Cantor is not even cited in the history section; Actual infinity is linked only for saying that ancient Greeks did not accepted this concept; etc. It is for starting to correct this misrepresentation of the mathematical concept that I have edited the lead. A deeper edit of the whole article would be needed, but it would need much more work.

It seems from the above discussion that the aim of my edit may be unclear for some editors. For clarifying this, I have added a phrase about actual infinity and its manipulation. I hope that this will make clear why the use of Grothendieck universes (actual infinity) in the proof of Fermat's Last Theorem is of a different nature from Euclid's proof of the infinity of the sequence of primes (potential infinity). I am convinced that the lead must make clear that actual infinity is not only commonly used, but is fundamental in modern mathematics. It is possible that my edit could be improved, but in any case, per WP:NPOV, the importance of actual infinity must not be minimized. D.Lazard (talk) 08:56, 10 October 2019 (UTC)

@D.Lazard: I think that it is an important concept and should be mentioned. I had removed it earlier because the actual link was a WP:SURPRISE and the topic is not really covered in the body. I agree that it's important enough to include in the lead at some point, although with clearer link context and perhaps after it is mentioned more thoroughly in the article. — MarkH21 (talk) 09:30, 10 October 2019 (UTC)

Zeno of Elea

Unless someone can defend the mention of Zeno in this article, I propose to delete the associated passages.

The lead mentions Zeno as one who speculated about the nature of the infinite. No documented speculations on the matter, however, are attributed to Zeno. His paradoxes are best understood in the context of the Eleatic rejection of the ideas of motion and change, not as positive advances over the philosophy of Parmenides, the founder of the Eleatic school, whose known views were quite unconcerned with the infinite.

Since the 17th century, consideration of the infinite has provided tools to resolve the paradoxes. This explains the recent association of Zeno with infinity, but it does not turn the paradoxes into speculations on the concept.

Similarly, the section § Early Greek attributes "attestable accounts of mathematical infinity" to Zeno. There are no such accounts in the known works of Zeno.

It is noted, correctly, that Aristotle called Zeno the inventor of dialectic. This fact has nothing to do with infinity and does not belong in the article.

Peter Brown (talk) 16:37, 10 October 2019 (UTC)

On the principle, I agree with you. However, for many people, Zeno's paradoxes are associated with infinity, or, more exactly with the fact that an infinite series may have a finite sum. Therefore, I suggest replacing the passages that you will suppress by a section that expands your sentence "Since the 17th century, consideration of the infinite has provided tools to resolve Zeno's paradoxes". This has to do with infinity, and thus belongs to this article. D.Lazard (talk) 18:02, 10 October 2019 (UTC)

Challenge accepted! However, since I have made no use of my mathematics and philosophy degrees in the last 30 years and I do not currently have access to an academic library, it will take me a bit to get up to speed on this. I will bear no hard feelings if some reader of this section makes the changes before I'm ready. Peter Brown (talk) 00:48, 11 October 2019 (UTC)

Edit war starting at Infinity (disambiguation) about the description of Infinity

See Talk:Infinity (disambiguation)#Description of Infinity. D.Lazard (talk) 16:28, 27 October 2019 (UTC)

The article is not well named

There is not really any such thing as infinity. It is therefore misleading to use "Infinity" as the name of an article. A truly encylopediac article would not start out with the qualification "In common usage…". Rather, it would characterize whatever the article title denotes or at least prepare the reader for such a characterization. When, as here, there is nothing denoted—not even something fictional—such a characterization is impossible and therefore has not been provided.

A widely held view, which I do not dispute, is that some things are infinite, the set of real numbers for example. Whether the universe is infinite in extent is certainly a coherent issue. The quality of being infinite, however, is infinitude, not infinity. The article perhaps should be renamed "Infinitude". This would need some reworking of the lead section and, of course, a redirect from Infinity to Infinitude.

To be sure, the word "infinity" is used meaningfully. Here are over one hundred samples. All such uses, though, are shorthand and do not imply the existence of something called "infinity".

When a variable is said to "approach infinity", "tend to infinity", etc., what is usually being described is the state of a system or the value of a dependent variable that is approached as a limit as an independent variable increases without bound. Some writers purport to describe the state of a system when the independent variable is "at infinity"; these really characterize a state that never actually obtains but which is approached as a limit as the variable increases without bound.

Another common use of the term is in the phrase "an infinity of". That phrase is equivalent to "infinitely many" and does not imply the existence of something called an infinity. Grammatically, the expression is plural, despite the singular article; one says "There are an infinity of natural numbers", not, "There is an infinity of natural numbers", at least not usually. Of course, the set of natural numbers does have a cardinality, ℵ₀, but that's another matter.

Peter Brown (talk) 05:08, 8 November 2019 (UTC)

It's an interesting point, though I think you've overstated it a bit. Not all meaningful uses are shorthand. An obvious class of exceptions is the ones that refer to the infinity of the extended real numbers. This is important, for example, in measure theory, where it is completely standard to say that the measure of some set is infinity, and this is not "shorthand" for anything.

That said, as I said on WT:WPM, I do think we need to put some serious thought into exactly what this article is about. I would also support a merger with infinity (philosophy), even though that arguably makes it even harder to figure out what it's about.

I suppose one possibility is to make it a WP:DABCONCEPT. I say that reluctantly because I'm not particularly fond of that class of article. But I'm struggling to figure out what else to do. --Trovatore (talk) 05:46, 8 November 2019 (UTC)

Do not forget that in some (not unusual) contexts of real analysis and topology "infinity" means, literally, the well-known point in the well-known one-point compactification of the real line. Or one of the two points $\pm \infty$ in the two-point compactification. And in complex analysis, one-point compactification of the complex plane. In such context, "tends to infinity" becomes, literally, convergence to this point. And "measure equals infinity" is also interpreted literally. As well as "the interval $[a,+\infty ]$ etc. (In projective geometry, embedding the plane into the projective plane, we observe rather "the line at infinity".) Boris Tsirelson (talk) 06:42, 8 November 2019 (UTC)

It's also certainly a notable concept, if not a "thing" (which seems to mean an object) that is used in projective geometry and measure theory. — MarkH21 (talk) 07:01, 8 November 2019 (UTC)

Britannica's lead may be useful to consider:

Infinity, the concept of something that is unlimited, endless, without bound. The common symbol for infinity, ∞, was invented by the English mathematician John Wallis in 1657. Three main types of infinity may be distinguished: the mathematical, the physical, and the metaphysical. Mathematical infinities occur, for instance, as the number of points on a continuous line or as the size of the endless sequence of counting numbers: 1, 2, 3,…. Spatial and temporal concepts of infinity occur in physics when one asks if there are infinitely many stars or if the universe will last forever. In a metaphysical discussion of God or the Absolute, there are questions of whether an ultimate entity must be infinite and whether lesser things could be infinite as well.

References

Paul August ☎ 11:56, 8 November 2019 (UTC)

All good ideas. Trovatore is surely correct about extended real numbers as are Tsirel and MarkH21 about compactification, projective geometry, and measure theory. If Infinity is redirected to Infinitude the latter will need some {{redirect}} entries such as

"Infinity" redirects here. For Points at infinity, see Extended real numbers and Compactification (mathematics).

The Britannica lead could be adapted to Infinitude but it needs some work. As it stands, it characterizes Infinity as a concept but, in some contexts, Infinity is a measure.

Peter Brown (talk) 19:41, 9 November 2019 (UTC)

I strongly oppose to move the page to Infinitude. The main reason is that this is an article on mathematics and infinitude is rarely used in mathematics. The term is not used in the article. The redirects Infinitude and Finitude have each only two links from the main space, and only one of these four links is in an article of mathematics. Wikipedia must reflect the common use; therefore, infinity must be called infinity, even if some people think that it is a misnomer.

About Peter's opening post. This is true that there is no mathematical object called infinity. This does not means that there is no mathematical concept called infinity. On the contrary, the term infinity appears in many mathematical phrases, such "tends to infinity", "point at infinity", "two parallel lines intersect at infinity", "hyperplane at infinity", "an asymptote is a tangent at infinity", "Taylor expansion around infinity", "property at infinity", ... Each of these phrases can be accurately defined without using infinity, but this does not mean that infinity is not a concept. This means that mathematicians are not philosophers, and try to avoid circular definitions. This means also that the concept of infinity has multiple aspects, that cannot be reduced to a single formal definition. Also, many of these phrases were in use a long time before a formal definition could be given.

About Encyclopedia Brittanica quotation. Infinity as a physical concept seems to be an error. Every occurence of infinity that I know in physics can be restated as the question whether the mathematical concept of infinity models correcly the physical reality.

About Peter's opening post. This is true that there is no mathematical object called infinity. This does not means that there is no mathematical concept called infinity. On the contrary, the term infinity appears in many mathematical phrases, such "tends to infinity", "point at infinity", "two parallel lines intersect at infinity", "hyperplane at infinity", "an asymptote is a tangent at infinity", "Taylor expansion around infinity", "property at infinity", ... Each of these phrases can be accurately defined without using infinity, but this does not mean that infinity is not a concept. This means that mathematicians are not philosophers, and try to avoid circular definitions. This means also that the concept of infinity has multiple aspects, that cannot be reduced to a single formal definition. Also, many of these phrases were in use a long time before a formal definition could be given.

About ∞ symbol: It is wrong that it is the mathematical symbol of infinity. It is the symbol of the infinity on the real number line. It is not used for infinite numbers nor for infinity in geometry (points at infinity). Therefore it must be removed from the first sentence of the article, and the section "Infinity symbol" must be adapted. D.Lazard (talk) 12:35, 10 November 2019 (UTC)

I'm convinced. The article must be called "Infinity" unless there's agreement that each the various notions (geometric, cardinal, ordinal, metaphysical, etc.) must be given its own article or article section, in which case Infinity should be a disambuation page.

I do disagree about $\infty$. I have never worked with the extended real numbers, but the symbol is very familiar to me as a pseudo-bound in expressions of limit, integration, infinite sums and products, etc. I would naturally read them out loud as "the integral from one to infinity of f of x with respect to x", "the limit of f of x as x tends to infinty", and so forth. I think that it is common to read $\infty$ as "infinity". The meaning of an expression is determined by the way it's commonly used, so ∞ is the symbol for infinity. Peter Brown (talk) 14:36, 10 November 2019 (UTC)

I think that D.Lazard point is that while ∞ is a symbol for infinity it is not the symbol for infinity, since in some contexts it is not used. Paul August ☎ 15:15, 10 November 2019 (UTC)

(Outdenting since I have no idea whom I'm replying to at this point). I don't want to get too caught up in all this, but maybe another thought is to have an "Infinity" article which would be a fairly general overview of the very broad concept, including most of what's currently at Infinity (philosophy), along with the stuff from this article from the "Physics" section onward. That article would then include a section on the use of infinity in mathematics, which would be a short summary of this article, which gets moved to "Infinity in mathematics" (along with a {{main}} pointer). The scope of this article can then be pinned down a bit better (infinite sets; infinity as a bound for limits, sums, integrals, etc; point at infinity in compactification; etc etc etc). Does this make sense? Is it a horrible idea? –Deacon Vorbis (carbon • videos) 16:07, 10 November 2019 (UTC)

I think that's actually a pretty good plan. -Trovatore (talk) 08:32, 15 November 2019 (UTC)

Ring or circle as symbol

In his recent edit, DavidCary is surely correct that the circle, or the ring, is a symbol of infinity (or perhaps eternity). This association definitely merits inclusion in Wikipedia. The choice of the Infinity article is plausible, though other choices might be considered. As Deacon Vorbis says, his contribution is somewhat off-topic for this article, but it is close enough that inclusion merits discussion, at least. It surely doesn't belong in § Arts, games, and cognitive sciences, but perhaps it can be given its own section?

Peter Brown (talk) 21:27, 7 September 2020 (UTC)

(Personally, I think that a circle has nothing to do with infinity. If it does, a square would qualify just as well.)

But seriously, given where the (way too many) sources come from, I don't think it deserves its own section in this article. If it does belong somewhere at all, then indeed the § Arts, games, and cognitive sciences would be the place, provided the section title is amended to § Arts, religion, games, and cognitive sciences - DVdm (talk) 21:45, 7 September 2020 (UTC)

(edit conflict) For better or worse, this article article focuses more on the somewhat more well-defined conceptualization of infinity in mathematics. For the more wishy-washy stuff, we have Infinity (philosophy), but I'd be hesitant to include this even there. The sources I saw gave only brief, off-hand mentions. In order to add something of value, it would have to say a bit about how a circle symbolizes infinity, which would have cultural manifestations other than just wedding rings. –Deacon Vorbis (carbon • videos) 22:04, 7 September 2020 (UTC)

The Dharmachakra and the Ouroboros, respectively from Indian and Egyptian traditions, are circular symbols representing unending (i.e. temporally infinite) cycles. § Arts, games, and cognitive sciences is already too miscellaneous. Philosophy is "wishy-washy"? The field gave rise to logic and natural science.
Peter Brown (talk) 00:41, 8 September 2020 (UTC)

1) Alchemy gave rise to chemistry, but that doesn't stop alchemy from being wonky. But more importantly, 2) Umm, I never even said philosophy was wishy-washy, but rather the article at Infinity (philosophy) deals with the vaguer, more wishy-washy aspects of infinity, whereas this article tends to deal with the more precise mathematical notions. I realize that's maybe not ideal, but it's just the way things are at the moment. –Deacon Vorbis (carbon • videos) 03:10, 8 September 2020 (UTC)

I would dispute that it's "the way things are". Of those mentioned in Infinity (philosophy), whom do you view as wishy-washy? Aristotle? Locke? Certainly, there have been careless philosophers, but they don't make it into Wikipedia. The article has no mention of the alchemists, for example. For thinkers who were unclear on their concepts, the views of l'Hôpital and Bernoulli, mentioned in the more mathematical article, are better examples.

This is of course beside the point. I am arguing in support of DavidCary's thesis that the circle, and I'll add the wheel, are symbols of eternity and infinity. I have mentioned the Dharmachakra and the Ouroboros in support.

@DavidCary:You really need to provide, not just citations, but arguments to show that your citations buttress your thesis. The Doniger book seems totally irrelevant and therefore dilutes the attempt at support. You have been most industrious in coming up with references, but they are mostly from modern authors who assert, without support or much elaboration, that the circle or ring has long been used to represent infinity or eternity. References to Christian literature are particularly doubtful since Christianity's sacred book starts out "In the beginning ...", implying that, unlike a circle, the world had a beginning. Deacon Vorbis refers you to WP:OVERCITE, which I also recommend that you read. Your thesis — which I do agree with — is not well supported by a multiplicity of sources, certainly not any that asserts our view in passing.

Peter Brown (talk) 23:01, 8 September 2020 (UTC)

Unicode v LaTeX for the symbol

I am not sure that we really need the infinity symbol in the first sentence, but if it is to remain, I sort of think PolarisBSH makes a decent point. One advantage for having the symbol there is that it's a convenient spot from which to copy the unicode. If we use <math>, that doesn't work. --Trovatore (talk) 23:36, 27 January 2020 (UTC)

Agreed. Unicode is preferable there. - CRGreathouse (t | c) 07:19, 29 January 2020 (UTC)

An editor thought I "preferred" the Latex version... actually, I hadn't seen the Talk discussion about cut-and-paste of the symbol, so pretty much arbitrarily chose the Latex version. In light of this discussion, I've changed it to the Unicode symbol. I see no reason to have three renderings in the lead, nor to point out that one of them is "(in unicode)". --Macrakis (talk) 14:36, 8 September 2020 (UTC)

I certainly killed the "in Unicode" bit (since the {{math}} version was still giving the straight character, just with a different font), but as I said in my edit summary, it's reasonable to present a reader with the various ways they might see it rendered on this page (or even elsewhere on WP). We've got a horrible patchwork of methods for rendering math, and this is just a mild concession to that fact. I've reworded it slightly so it doesn't clutter the opening sentence and to make it clear that it's the same symbol, just rendered differently. –Deacon Vorbis (carbon • videos) 14:49, 8 September 2020 (UTC)

The fact that we have three ways of writing the infinity symbol internally is really not the reader's concern. The extremely minor differences in appearance between the three methods aren't worth mentioning, any more than the article on the letter 'b' says that it may look like b, b, or b in the lead.

I do understand the motivation for having a copyable letter rather than an image, but the reader has no way of knowing that $\infty$ is an image rather than a character, so that requirement isn't met.

There is more of an argument for presenting the different glyphs and different ways of writing the symbol in the Infinity symbol article, but even there, using the three internal ways in the lead is unnecessary. --Macrakis (talk) 15:14, 8 September 2020 (UTC)

I also agree that we don't need to show the various renderings and fonts for the infinity symbol in this article. Just pick one copyable symbol. Having three of the same symbol is unnecessary clutter. Readers who are interested in the forms of the symbol itself can go to the article on the symbol. — MarkH₂₁^talk 15:26, 8 September 2020 (UTC)

@Peter M. Brown and Deacon Vorbis: Any objections? --Macrakis (talk) 16:31, 9 September 2020 (UTC)

Yes, but it would appear I'm in the minority here, so I'll probaby just have to live with it. But if you're going to simply use one, it should probably be with {{math}}, as ∞, since it tends to look better. –Deacon Vorbis (carbon • videos) 16:41, 9 September 2020 (UTC)

Not clear that you're in the minority. MarkH21 and I are for choosing 1 symbol; you are for 3; and Brown seems to be for 3 (based on Edit summary). @Trovatore and CRGreathouse: you may wish to comment.

I think we need to be more explicit about our reasoning so that we can discuss productively. Here is mine:

1) Users don't see the varying internal mechanisms, only the visible result.

2) The visible results are very similar, at least as similar as various glyphs for the same alphabetic letter in different fonts. Except in cases where there are structural differences in shape (e.g., the two-counter a vs. the one-counter ɑ), WP doesn't usually comment on such variants.

3) In any case, the shapes will vary based on the OS, browser, and Wikipedia defaults, so it's not as though we can demonstrate the different shapes in a useful way. In fact, in some configurations, they may be identical, which will be even more confusing. If we do need to demonstrate graphic variants (which I don't think we do, certainly not in this article), that can only be done reliably with images, not with textual markup, as is done in the Infinity symbol article, like this:

4) If we do comment about such variants, it's in the article about the symbol (in this case Infinity symbol), not about the concept.

5) We also comment about variants if there is a semantic difference, as in ϕ vs. φ, where the variants (perversely) mean different things in math. But here there is no semantic difference among the variants.

6) As User:Trovatore and User:CRGreathouse point out above, it's a nice courtesy to the user to give a copyable version, so that would be ∞ ({{math|∞}}) or ∞ ({{big|∞}}) rather than $\infty$ (<math>\infty</math>).

Agreement? Rebuttal? --Macrakis (talk) 18:05, 9 September 2020 (UTC)

I am for at most one symbol, at least in the first sentence. I'd be OK with zero. I would mildly prefer to make it copyable; no point in frustrating people when you don't have to. But I don't care that much. I do think multiple, nearly identical versions of the symbol in the first sentence is a bad idea, and on that point I care a bit more. --Trovatore (talk) 18:55, 9 September 2020 (UTC)

The lead, with three symbols, scans well. I don't understand why this is a bad idea in itself. It's true, though, that — if there are multiple versions — it's unfriendly to omit indicating anywhere that one can be copied. Once upon a time, the article did say that ∞ was Unicode, as Infinity symbol does now, which indicates to the sufficiently knowledgeable reader (but not to others) that this version could be copied.

∞ is too tiny, however, and ∞ is ugly. Except at Infinity § Symbol, the article uses the better-looking <math>\infty</math> symbol everywhere. Do we need to say, explicitly, that ∞ can be copied, at Infinity symbol if not in the Infinity article itself? Just a suggestion: how about leaving the text of the Infinity symbol article alone but noting in the {{infobox}} legend that the symbol can be copied from there?

Peter Brown (talk) 20:37, 9 September 2020 (UTC)

I really don't think the lead "scans well". Three slightly different versions of the same symbol strikes me as remarkably silly. I don't want to get hyperbolic on this issue because the whole thing doesn't matter that much, but three versions is the worst possible option. --Trovatore (talk) 22:16, 9 September 2020 (UTC)

I concur with Trovatore (on most everything, but in particular) that one symbol should suffice. I think being copyable is important. - CRGreathouse (t | c) 01:21, 10 September 2020 (UTC)

OK, lets use {{math|∞}}. The template discussion calls {{math}} "an alternative to using the <math>...</math> tag pair" so I wasn't distinguishing {{math|∞}} from <math>\infty</math> and didn't realize that the former could be copied. I'm mildly unhappy that it differs from nearly every other use in the article, but let's go with it. Deacon Vorbis, do you want to do the honors, since you've been editing it? Peter Brown (talk) 02:24, 10 September 2020 (UTC)

I'm sort of doing ten things at once right now. I'll look at it tomorrow probably when I can properly fret over the wording, but if anyone wants to in the mean time, that's totally fine. –Deacon Vorbis (carbon • videos) 02:29, 10 September 2020 (UTC)

I've the simplest thing. Perhaps others can improve on it. --Macrakis (talk) 17:48, 10 September 2020 (UTC)

Usage pre-19th century in geometry

@D.Lazard: The following sentence in the "Geometry" section is a bit strange:

Until the end of the 19th century, infinity occurred rarely in geometry.

I think I understand what you mean, but it's a bit misleading or just incorrect as currently worded. It's not like people didn't use analytic geometry following Descartes (essentially with real numbers, but at least over the rationals or ${\overline {\mathbb {Q} }}$) or that they didn't view lines as extending infinitely. — MarkH₂₁^talk 12:51, 2 February 2021 (UTC)

I agree that the sentence is a bit curt and deserves better treatment. But I am not aware of any studies of geometric infinity before the 19th century. Aristotle was clear that lines could be extended indefinitely as needed ("potential infinity"), but he insisted that they never reached "actual infinity." In other words, lines must not be considered to actually extend forever, but you could keep drawing them however long you needed. Mathematicians largely followed his advice up until the 19th century. On the other hand, mathematicians did consider the number of points on a line (segment) to be infinite, even if it did not extend to infinity. Galileo famously pondered the "paradox" of having the same infinite number of points on two segments of different lengths. But he did not resolve the paradox, nor did he claim (as far as I know) that lines extended to infinity. --seberle (talk) 11:20, 8 February 2021 (UTC)

I agree. About the points on a line: As far as I know, the geometers did not considered that a line is composed of points. So, it was not the number of points on a segment that was infinite, but the number of possible positions on the line of a single point. A witness of this is the expression "locus of a point that" instead of "locus of the points that" (the plural was nonsensical before 20th century). D.Lazard (talk) 12:16, 8 February 2021 (UTC)

Now that is interesting! I learned something today; thanks very much. I read my dad's old college math texts when I was a kid, and they used this "locus of a point" phraseology. I never realized it had this significance till today.

Still, infinity in geometry isn't just infinite sets; there's also the point at infinity, and the commonplace that "parallel lines meet at infinity". Our article on projective geometry dates its formalization to the 19th century as well, but what about its pre-formal versions? I'm not great at history and don't have a good sense of how, say, da Vinci might have seen this, in his work on perspective. --Trovatore (talk) 18:28, 9 February 2021 (UTC)

That is true. The only example I know of someone seeming to consider the points (or positions) on a line was in the case of Galileo, which I mentioned above. If I remember correctly, he noticed you could match the points in short segment with the points in a longer segment by drawing segments between them. I think I need to go back to the original and refresh my memory on exactly what he did and whether he referred to "points" on the line or "positions" or what. --seberle (talk) 16:35, 9 February 2021 (UTC)

I have boldy expanded the first sentence into a paragraph. Be free to improve it and/or tagging is with {{citation needed}}. D.Lazard (talk) 18:28, 9 February 2021 (UTC)

The edit looks good. (I'll probably make some minor grammar/style edits.) I still wonder if we should include something on Galileo's Paradox as an exception, showing that some were aware of a primitive idea of an infinite set of points. (Wikipedia has a whole article on Galileo's Paradox.) Galileo did, in fact, repeatedly refer to lines "containing an infinite number of points." --seberle (talk) 07:44, 10 February 2021 (UTC)

Oh, and this entire section is lacking citations. We need to add references. --seberle (talk) 08:36, 10 February 2021 (UTC)

Explanation

@Peter M. Brown:, the reason why I removed those words is because it says "on the right" which is not the case when viewing the page on mobile device. On phones, the picture is shown just below the text, not on the right side as in a computer. I thought it would create a confusion. ☎️ Churot ^DancePop 16:20, 23 February 2021 (UTC)

Well noted. "... on the right" won't do. Peter Brown (talk) 17:11, 23 February 2021 (UTC)

"Unboundedness" listed at Redirects for discussion

A discussion is taking place to address the redirect Unboundedness. The discussion will occur at Wikipedia:Redirects for discussion/Log/2021 February 25#Unboundedness until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 𝟙𝟤𝟯𝟺𝐪𝑤𝒆𝓇𝟷𝟮𝟥𝟜𝓺𝔴𝕖𝖗𝟰 (𝗍𝗮𝘭𝙠) 21:39, 25 February 2021 (UTC)