Talk:Infinity

In Our Time

The BBC programme In Our Time presented by Melvyn Bragg has an episode which may be about this subject (if not moving this note to the appropriate talk page earns cookies). You can add it to "External links" by pasting {{In Our Time|Infinity|p0054927|Infinity}}. Rich Farmbrough, 03:16, 16 September 2010 (UTC).

Finity symbol ?

If the double circle is the symbol for infinity, what is then the symbol for finity; ie a single circle with a stripe in the middle, spiral, spriraling in clockwise (think I've seen this as symbol for Tangata-Manu) ? —Preceding unsigned comment added by 91.182.136.235 (talk • contribs) UPDATE: see http://en.wikipedia.org/wiki/User_talk:Jeff_Dahl#Finity_symbol —Preceding unsigned comment added by 91.182.227.62 (talk) 07:32, 24 September 2010 (UTC)

Please do not go adding symbols for "finity" to the article, unless you can find them in reliable secondary sources. I have never heard of a standard symbol for "finity", nor for that matter do I recall ever encountering the word.

It may be that you are not familiar with our procedures. One of the most fundamental ideas is that in writing an encyclopedia, you are not allowed to make anything up. Encyclopedic writing is a very conservative form; there is some creativity to be found in choice of language or organization, but essentially none is permitted in the content. In the case of an encyclopedia that anyone can edit, it is especially important to make sure that others can verify where your information comes from.

Some links that may help you: Wikipedia:No original research, Wikipedia:Verifiability, Wikipedia:Reliable sources. --Trovatore (talk) 07:49, 24 September 2010 (UTC)

This looks like a joke comment. Besides, it was off-topic on this article talk page. If it was no joke after all, then it belongs on the math ref desk. DVdm (talk) 16:03, 24 September 2010 (UTC)

I dunno, it seems more like confusion to me. "Finity" is not actually a word of course. The proper term, would be "Finite." I believe the confusion is on the nature of the word and how we use mathematical symbols. We do not need a finite symbol, simply because everything, as far as we know, is finite. One of those things like how you dont add a + in front of positive numbers. Basically, the symbol for "Finite" would be a lack of the symbol for infinite, since basically anything can be considerd finite until noted otherwise. 74.128.56.194 (talk) 21:09, 15 May 2011 (UTC)

Sizes

It is critical to point out that Cantorian cardinality is a notion of size. Then criticisms of that viewpoint may be introduced. But it is not helpful to just call them different "kinds", without noting that what makes them different, according to the overwhelmingly dominant conceptualization, is their size. --Trovatore (talk) 17:51, 7 October 2010 (UTC)

Good idea, but it also needs to point out that such different sizes exist within, and relative to, Cantor's formalism. In this way, one need not make any ontological commitments that a significant section of the readership may disagree with. Tkuvho (talk) 17:58, 7 October 2010 (UTC)

First, it's inappropriate to speak of "Cantorian formalism". Cantor had no formalism.

Second, you don't have to make ontological commitments. Cardinality is a notion of size whether or not you think anything having that size actually exists. --Trovatore (talk) 18:01, 7 October 2010 (UTC)

The previous sentence speaks of Cantor having "formalized" the notion of infinity in terms of set theory. Cantor certainly did have a formalisation, ask all the freshmen struggling to understand it :) I don't see how you can make an absolute statement about cardinality. It is a notion that exists relative to Cantorian set theory. Alternative theories exist that would have no room for statements such as "infinities come in different sizes". Tkuvho (talk) 18:06, 7 October 2010 (UTC)

No, Cantor did not have a formalization. He worked in informal terms. In his view he was simply speaking the truth, and showing why it was true. Hypotheses non fingo, dixit.

Yes, such alternative theories exist. They are severely minoritarian viewpoints. They should be treated, but not as the first point mentioned. --Trovatore (talk) 18:13, 7 October 2010 (UTC)

Fwiw, I have added a source for "infinite sets of different sizes". I propose we dump the "formalism" word unless we have a source for it, i.e. a source that uses "Cantor", "infinite", "set" and "formalism" in sufficient proximity, so to speak. DVdm (talk) 18:55, 7 October 2010 (UTC)

I don't really think a citation is needed here -- any citation for that should go in cardinality. I've also reworded, but more work will be needed: I think we're all agreed that "formalism" should go. CRGreathouse (t | c) 20:12, 7 October 2010 (UTC)

"Formalism" is not the right word as it implies a connection with Hilbert's approach, which would be ahistorical. Since, as we state, Cantor formalized the notion of infinity, we can certainly speak of Cantor's set-up, or his theory, or whatever. Cantor's approach is the majority approach in contemporary mathematics, but mathematicians do not have a monopoly on infinity. Physicists have been doing just fine for centuries, working with notions of infinity and not assuming anything like the powerset construction. Similarly, before Cantor mathematicians like Gauss and Dirichlet were doing just fine producing perfectly rigorous mathematics, so assuming that Cantorian set-up is the foundation of reality is somewhat reductive. This is why I think we should relativize any claims about sizes of infinity in the introduction, by making them contingent on Cantor's formalisation/set-up/theory, and avoid making absolute statements about the existence of such sets. Tkuvho (talk) 08:17, 8 October 2010 (UTC)

Unexplained and unwarranted revert...

hello. You seem to have a disagreement with my recent edit(s) on the "Infinity" article. Not sure why. You said "not helpful" though you knew they were "good-faith." You didn't really explain HOW they were supposedly a "not helpful." (By the way, you also removed a separate edit, the first one, a simple citation reference, that was put in by me, per tag request...)

To be frank, it's in violation of Wikipedia policy when you revert accurate and good-faith things, with no valid explanation. Only vandalism or truly inaccurate (or unrelated) additions should be summarily "reverted."

But you removed edits that were very accurate, sourced, as well as "good-faith." (Along with even a simple citation that was per tag request...)

Why? Like I said, you also removed a needed citation reference, in the first paragraph.....in response to tag requests. Why remove that too? Sweeping everything away in one shot, with no valid explanation...simply because YOU didn't like the other edit. Also, it's arguably in violation of WP:Ownership.

WP policy says "reverting" should RARELY be done...when in doubt, DON'T, it says. (As seen in WP:ROWN, WP:1RR, and WP:0RR) Otherwise, please take it to the article talk page..

A needed citation per tag request is "helpful", not just "good-faith"....you reverted that as well......with no valid reason.... also you didn't explain how the other edit was "not helpful". I hope we can work this out... let me know your thoughts. Thanks. ResearchRave (talk) 02:15, 17 October 2010 (UTC)

Edits on mathematical topics are best carried out by professional mathematicians. Xxanthippe (talk) 02:24, 17 October 2010 (UTC).

Sorry, XX, but that remark itself was "not helpful", but was evasive, and doesn't really address anything specific. Honestly, what you just said is in SUCH violation of Wikipedia policy, it reeks of arrogance, elitism, and rudeness...

What you did was basically give a non-response response, with no details on what specifically was supposedly wrong with the edits... Why? You didn't address any specifics, but instead were DISMISSIVE. Also, in your revert comment about the dictionary reference source, all you said was that it was "misleading" or something. Maybe it was, I don't know....but you didn't exactly explain how.

Wikipedia policies
Article standards
Neutral point of view Include only verifiable information No original research Citing sources What Wikipedia is not
Working with others
Assume good faith Civility and etiquette No personal attacks Resolving disputes No climbing the Reichstag dressed as Spider-Man

I mean, is that website maybe "not reputable" enough or something? But to say that articles like this should best be carried out by professional mathematicians, in violation of WP:Ownership, WP:COI, Etiquette, Neutrality, etc, arguably, then that's elitism, and suppression, and not really any longer a true "wiki", at least not with certain articles. My edits were valid, good-faith, accurate, and should have stayed, plain and simple. You have yet to say anything AT ALL specific, on how any of them were "not helpful" or were "misleading". You simply asserted that they were so. Not good enough. If you could maybe elaborate your assertions, I might be able to understand. If not, then I would just have to assume that you violated WP policy on various levels, with no real policy backing, and just hope to get away with it....peace out. ResearchRave (talk) 02:42, 17 October 2010 (UTC)

It's true, I'd consider that site less-than-reputable, but my revert was just because thesuch a reference doesn't belong here but at another project like wiktionary. Also, it adds no real information to the article.

As far as policy goes, I'll see your WP:N and up you a WP:CONS.

CRGreathouse (t | c) 03:10, 17 October 2010 (UTC)

Alright, well I'm not sure why necessarily that site would be considered not all that reputable. And yes, I know about consensus, but that's not really one of the main "pillars" of WP. Though I know that's important too. By the way, when you said "I'll see your WP:N", I'm not sure if you meant that "Notability" was something I wasn't following (because WP:N is referring to Notability), or if you meant rather my argument for "Neutrality" (or WP:NPOV). But either way, I know that consensus is one of the policies too.... ResearchRave (talk) 03:21, 17 October 2010 (UTC)

Yes, I know the pillars. CRGreathouse (t | c) 03:37, 17 October 2010 (UTC)

Well of course. Yes, I know...but I was asking why you brought up the "Notability" thing... Did you mean that I was not following the "Notability" policy, in my sources or edits? ResearchRave (talk) 04:19, 17 October 2010 (UTC)

Are you discussing Isaac Asimov's comment that infinity is not a number? That in itself is a controversial claim that contradicts material already contained in the lead. Tkuvho (talk) 05:38, 17 October 2010 (UTC)

I don't see how it "contradicts" anything in the lead, as right in the very paragraph already, where I (attempted to) put the point, it said ALREADY previously these exact words "it is not the same sort of number as the real numbers." What I tried to put in fit RIGHT ALONG with that. If it didn't, can't you maybe explain just how not? And where exactly would there have been any actual "contradiction"? The article itself says fairly clearly that "infinity" is "not a real number."

Also too, in the very first paragraph, it says that infinity is a "concept" that is "without end." What I tried to put was "a quality of endlessness." Or "concept of endlessness." ... exactly what was said in the lead itself. So I'm a little confused by what you just said.... Can you please clarify? Thanks... ResearchRave (talk) 10:18, 17 October 2010 (UTC)

Endlessness is fine, but we already mention that it is a quantity "without bound or end". Why do we need Asimov to tell us this? It may be interesting to include speculations of this sort from Leibniz, who may be more of an authority. Tkuvho (talk) 10:54, 17 October 2010 (UTC)

Asimov is amazing -- one of my favorite authors -- but his quote on this matter is terrible. But that makes some sense, given the context: a book for trying to get kids 'hooked' on math. CRGreathouse (t | c) 13:29, 17 October 2010 (UTC)

Integral from -∞ to +∞

Saying the integral from -∞ to ∞ represents the total area under the graph isn't strictly accurate- that quantity is defined as the limit of a sequence (or more strictly two sequences, as the lower limit of the integral tends to -∞ and the upper to ∞). The concept of "total area" on an infinitely long line is a little fuzzy, which is precisely what this article's about. Therefore changing it- comment here if you disagree, please. MorkaisChosen (talk) 12:34, 11 May 2011 (UTC)

I do disagree. It's a matter of terminology: the integral from -∞ to ∞ is finite, while the integral from -n to n is bounded. The area doesn't 'tend' to anything -- it's not changing. CRGreathouse (t | c) 16:05, 11 May 2011 (UTC)

I'm not a fan of this section. The notion of area under a curve is typically defined by an integral, not the other way around. I'd prefer to see a link to the Improper Integral article along with a statement along the lines of "An intuitive interpretation of the meaning of the following integrals is as follows:". — Preceding unsigned comment added by 76.181.83.8 (talk) 02:06, 6 June 2011 (UTC)

Removed unreference statement about turning an "8" on its side

This unreferenced statement is most likely false. Please read the section Typesetting#Letterpress era and look at "Diagram of a cast metal sort." Also, look at the full-sized photo of "Movable type on a composing stick on a type case" (photo at top of article). In both of these, you will see that a cast metal sort (a letter or character of moveable type) is rectangular in shape. Hence, there is no way that you can put a cast metal sort for an "8" on its side to obtain the infinity symbol. It would take a separate cast metal sort to obtain this symbol. — Preceding unsigned comment added by RJGray (talk • contribs)

No problem removing it. I did find a reference to a remark about typesetting an "8" on its side here, but it is related to a Dan Brown book, and I don't think that DB is a proper wp:RS. Perhaps digging deeper might reveal something. Or perhaps not. DVdm (talk) 21:28, 21 October 2011 (UTC)

Mythology

Removed the following text from the Cosmology section, because it is no more relevant to the subject of the article than other myths describing things being finite.

"In ancient cosmologies, the sky was perceived as a solid dome, or firmament."

Elroch (talk) 16:22, 4 December 2011 (UTC)

Symbol in lead

Minor issue, but nevertheless...

I had changed the symbol in the lead from "∞" (<big>∞</big>) to "$\infty$" ("<math>\infty</math>), as I thought it looks much better that way. The HTML rendering gives sort of a floating symbol, whereas HTML without the <big> tag produces "∞", a symbol that is too small. The symbol was changed back to the floating —and i.m.o. ugly— "∞" by user CRGreathouse (talk · contribs). Thoughts anyone?

As it happens I had roughly the reverse experience -- the LaTeX didn't line up quite right in the lede and looked wrong, so I changed it back to the Unicode. If there's consensus for the LaTeX (well, really BlahTeX I think) version I have no problem with it. CRGreathouse (t | c) 19:31, 11 December 2011 (UTC)

Ha... that information has triggered a few experiments here. It seems to be directly related to chosen setting in "My preferences, Appearance, Math". I use the setting "Recommended for modern browsers", which, in this case, has the same effect as "HTML if possible or else PNG" and as "MathML if possible (experimental)". When I try "Always render PNG" the symbol gets large and slighly floating indeed, although less than the HTML rendering. Strange, very strange. :-) - DVdm (talk) 19:48, 11 December 2011 (UTC)

Did some more tests — different system, same OP, same version of IE8, completely different behaviour. "∞" (<big>∞</big>) looks perfect here. Sigh... let's forget about this, sorry. - DVdm (talk) 07:23, 12 December 2011 (UTC)

The Infinity Symbol Image

I just had a look at this article and my first impression is that the picture is a tad unnecessary. Perhaps a single infinity symbol, but in multiple typefaces? Would it be better perhaps to consider just using a single typeface, or some other representation of infinity? I feel it detracts from the article. CorwinNewall (talk) 05:31, 14 February 2012 (UTC)

Isha Upanishad Quote

I would like to argue that the Isha Upanishad quote is not appropriate here. First, there are many translations of this particular verse. Second, infinity, or the idea of innumerability, is not necessarily what is implied. The work is more accurately referring to "all that is", not the mathematical sense of infinity. I am afraid that some unknowing individual will assume, as I did before investigation, that Isha Upanishad is a mathematical work when it is in fact a philosophical one. There should at least be a note of this. — Preceding unsigned comment added by 71.194.209.115 (talk) 03:56, 4 March 2012 (UTC)

This article is about the notion of infinity in general; it is not limited to strictly mathematical conceptions. So that the Upanishad is not a work of mathematics does not in itself disqualify it. However, if a selective translation is being used to shoehorn a mention in, that's a more serious matter. Can you tell us more about the translation issue? --Trovatore (talk) 08:07, 4 March 2012 (UTC)

Begin with this page (http://swamij.com/upanishad-isha-purna.htm). Next, look at the invocation here (http://www.stephen-knapp.com/sri_isha_upanishad.htm). And lastly the first translation here (http://www.vedabhoomi.org/SriAdiSankaracharyaBhasya.html). Each of these refers to the same portion of text, but translates it differently. I'll be happy to look through my library for some more convincing information over the next couple of days. Also see the link to the Yajurveda on this wiki page (http://en.wikipedia.org/wiki/Yajurveda). The composition date there is said to be 1000 to 1400 BCE whereas on the infinity page it is said to be 4th to 3rd century BCE. Neither is supported by a source. From my research thus far, I can not be certain which it is. — Preceding unsigned comment added by 71.194.209.115 (talk) 03:40, 5 March 2012 (UTC)