Talk:Infinity/Archive 3

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.^[1]"

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

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)

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)

Finity is a word, according to Merriam-Webster (though you have to Google "http://www.merriam-webster.com/dictionary/finity" and then click its link on the results page to see Merriam-Webster's definition of finity, otherwise they tell you that you must access Merriam-Webster Unabridged to see it). It's a synonym for finitude, similarly to how infinity can be a synonym for infinitude (see their Merriam-Webster definitions as well).SoccerMan2009 (talk) 03:28, 18 June 2012 (UTC)

There is a current conflict between two versions of the opening sentence,

Infinity (symbol: ∞) is the distinguishing property of something that has no limit,....

versus

Infinity (symbol: ∞) refers to something without any limit,....

Those who support the the first version argue, correctly, that Wikipedia articles should talk about the referent, not the word. I agree with that.

The problem is the use of the word property. Whatever infinity is, or even whether infinity exists, it is not a property. If it were a property, you would talk about, say, the stars' infinity, as you might talk about the stars' brightness or temperature. But this is a very minor usage and is surely not the topic of the article.

So the opening sentence needs to talk about infinity more as a concept or object (or related group of conceptual objects) than as a property, without being too specific about what sort of object. I think concept is a good word.

I would try something like the following:

Infinity (symbol: ∞) is a collection of related concepts involving the absence of limitedness....

I don't like everything about this proposed sentence but I think it's better than either of the versions being fought over. Improvements welcome. --Trovatore (talk) 20:36, 26 June 2012 (UTC)

Oops, sorry, I just reverted without checking the talk page first. I agree with the above comments of Trovatore. I am not happy with the sentence I keep reverting back to, but the use of property in the attempts to fix it, is just wrong! Each time I've reverted I have tried to come up with a better replacement and have failed. Part of the problem is that this term is so often misused that I want to be very careful about what is said about it. One certainly doesn't want to get into the philosophical debate about the existence of "completed infinities", at least not in the first sentence. Trovatore's suggestion, a valiant attempt, has much to be said for it (in particular, it is correct), but it is a little too "wishy-washy" for my taste. Perhaps something more like -

Infinity is a mental construct employed when discussing objects or concepts that are not limited ...

Potshots expected. Bill Cherowitzo (talk) 23:09, 26 June 2012 (UTC)

Well, "mental construct" is not really philosophically neutral either; it appears to deny the possibility that infinity exists independent of our reasoning about it. --Trovatore (talk) 23:20, 26 June 2012 (UTC)

That's unintentional. I was only looking for a way to sharpen up the phrase "collection of interrelated concepts" without changing its meaning. Bill Cherowitzo (talk) 23:39, 26 June 2012 (UTC)

The #Computing section of the article currently says the following:

The IEEE floating-point standard specifies positive and negative infinity values; these can be the result of arithmetic overflow, division by zero, or other exceptional operations.

Some programming languages (for example, J, UNITY and JavaScript) specify greatest and least elements, i.e. values that compare (respectively) greater than or less than all other values. These may also be termed top and bottom, or plus infinity and minus infinity; they are useful as sentinel values in algorithms involving sorting, searching or windowing. In languages that do not have greatest and least elements, but do allow overloading of relational operators, it is possible to create greatest and least elements.

In the second paragraph, the claims about J and UNITY are tagged as needing citations; a reference has been given for the JavaScript claim (Standard ECMA-262: ECMAScript Language Specification, sections 8.5 and 11.8.1–5). But this reference essentially says that JavaScript (well, ECMAScript) uses the IEEE floating-point standard (IEEE 754) for its Number type, with the exception that the various distinct NaN values defined in IEEE 754 are not necessarily distinguishable in ECMAScript.

So it seems to me that the "positive Infinity" and "negative Infinity" values in JavaScript are just IEEE floating-point infinities (or at least concepts inherited by ECMAScript from the IEEE floating-point infinities), which are discussed in the first paragraph of this section. The second paragraph is apparently talking about something different, explicit "greatest element" and "least element" values that are not just IEEE floating-point infinities. (I don't know J or UNITY, so I can't say for sure how these values behave.)

There is nothing particularly special about JavaScript's "positive Infinity" and "negative Infinity" values—any language or system that uses IEEE floating-point (i.e., most systems in use today, as far as I know) has these values too. JavaScript isn't special in this regard, and it seems to me strange and misleading to single out JavaScript as an example of the "some programming languages" that have greatest and least elements—if we count JavaScript's IEEE infinities as "greatest and least elements", then every other system using IEEE floating point also has "greatest and least elements". In any case, IEEE infinities were discussed in the first paragraph, so there's no need to repeat them in the second; I think the second paragraph is supposed to be talking about something else.

Other thoughts? —Bkell (talk) 06:36, 2 September 2012 (UTC)

First of all: I neither have knowledge about the nature of the values in question in J & UNITY, and how they are supposed to differ from IEEE-based implementations.

But I was under the impression that most programming languages did not really support infinity values, even if they might implement the IEEE floating-point standard, and this is partly true.

The C specification did not originally specify implementation details of the floating point system (including whether it has infinity values, or not)^K&R and neither does its current version require IEEE-compilant floating points. The C++ standard does not explicitly require the existence of the positive infinity value (but does require that it exist if the implementation environment is IEEE-compilant.)^§18.3.2.4 Although some versions and implementations of Python might support infinity values, it is not standardized, and work on the language feature has stopped.^PEP-754 Perl does not seem to support infinity values as language constants, but they can be synthesized by overflowing a floating point operation.

On the other hand, Java and C# explicitly require that the floating point types implement negative and positive infinity, and define that they are ordered as one would mathematically expect.^{§4.2.3§14.9.2} PHP seems to support infinity values (pre-defined constant INF), and has had an API for checking for the finity of a floating-point value since version 4.2.0.

In summary, even if the IEEE floating point standard has been around for 27 years, its adaptation in actual programming languages is still incomplete.

Another content question is that whether the language of the first paragraph (that talks about the IEEE standard) actually somehow excludes the examples of the second paragraph. Are J and UNITY somehow different from IEEE-compliant languages in their treatment of positive and negative infinity, or could an implementation actually just use IEEE floating points to represent these values? If the latter is true, then Java, C#, JavaScript and PHP (although PHP is not a specified language) should be just as good examples for the second paragraph, because the IEEE values behave just like claimed ("greatest and least elements, i.e. values that compare (respectively) greater than or less than all other values. These may also be termed top and bottom, or plus infinity and minus infinity; they are useful as sentinel values in algorithms involving sorting, searching or windowing.") You wrote"the second paragraph is apparently talking about something different", which might or might not be actually supposed by the article text.

Any comment from the original contributor? --hydrox (talk) 23:16, 2 September 2012 (UTC)

Yes, you're right; many programming languages themselves do not guarantee IEEE floating point, and often do not provide explicit access to the strange values like the infinities and NaN. This is usually because the language specifications are meant to be more or less implementation-independent, and there's no guarantee that the implementation is going to be using hardware with IEEE floating point.

If we want to point out languages that provide explicit access to the IEEE infinities, I think those should be made in the first paragraph, something like this:

The IEEE floating-point standard specifies positive and negative infinity values; these can be the result of arithmetic overflow, division by zero, or other exceptional operations. Some programming languages, such as Java, C#, and JavaScript, provide facilities to access and manipulate these infinity values.

—Bkell (talk) 03:45, 3 September 2012 (UTC)

Yes I agree that this section needs work. What you wrote sounds a good start, and I agree that examples of languages using IEEE floating points are more suited to the first paragraph. There's apparently a wealth of information available on J programming, including a free interpreter. I will try to find time to figure out how are infinity values used in J to make sense of the second paragraph (J language expert input also welcome) --hydrox (talk) 19:06, 5 September 2012 (UTC)

Turns out J uses hardware floating point values (i.e. IEEE floating points) to express infinity. ^19.2 It's treatment of infinity does not seem to differ in any way from that of Java, and JavaScript, and so there doesn't seem to be any basis for claiming that IEEE FP's would be somehow "different".

I edited the section to say that Java and J are good examples. C# I didn't include because I did not find anything that would say it actually provides explicit access to the infinity value (similar to Java's Float.POSITIVE/NEGATIVE_INFINITY, or JavaScript's and PHP's Infinity and INF constants), although it does define the existence of such value as result of some operations. Comments welcome. --hydrox (talk) 18:58, 6 September 2012 (UTC)

The new wording is much improved. Thanks for your investigative work! —Bkell (talk) 00:30, 7 September 2012 (UTC)

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)

I think that space cannot be infinity. There is always possipility to be someone like you, in our planet, but possipility that is very small, something like one of 90^90 of peolpe are just exalty like you. So, if space is infinity, so there is infinity possiple places there is same or smaller ratio, but still being ratio, wich means is possiple to there is guy exalty like you. Right? Still this is not full fact. If there is possiple to happen everything, so it means everything possiple happens everytime. One possiple event is also to someone makes machine that breaks somehow all knew and hidden natural physic laws, wich means we are exist and do not exist same time.

Good this is headspinning. ~Numberphile fan~ — Preceding unsigned comment added by 87.236.228.7 (talk) 17:56, 14 July 2013 (UTC)

I have removed the "minus one twelfth" nonsense. Even with that source it still remains nonsense. Comments? - DVdm (talk) 15:20, 4 February 2014 (UTC)

This is usually justified by means of Abel summation. Tkuvho (talk) 15:51, 4 February 2014 (UTC)

No, it's not Abel summable. The series diverges properly to ${\displaystyle +\infty }$. Sławomir Biały (talk) 01:15, 10 February 2014 (UTC)

FWIW - Thank you for the comments - I don't know if my edit, based on a recent WP:Reliable Source, is entirely ok or not - but seems worth a discussion:

Copied from the Infinity lead:

Interestingly, the summation of all natural numbers to infinity is "minus one-twelfth".< ref name="NYT-20140203">Overbye, Dennis (February 3, 2014). "In the End, It All Adds Up to –1/12". New York Times. Retrieved February 3, 2014.</ref>

${\displaystyle \sum _{n=1}^{\infty }n=-{\frac {1}{12}}}$

ALSO - A relevant video (07:49) by Numberphile "proving" the notion is at the following => http://www.youtube.com/watch?v=w-I6XTVZXww

In any case - Comments Welcome - and - Enjoy! :) Drbogdan (talk) 16:05, 4 February 2014 (UTC)

Yes, I had seen that video a few days ago, and I didn't find it interesting. I found it rather silly. - DVdm (talk) 16:11, 4 February 2014 (UTC)

@DVdm - Thanks for your comments - nonetheless, the basic issue is whether this particular notion is True - or not - if True, then is the notion worth adding to the Infinity article - or not - Thanks in any regards - and - Enjoy! :) Drbogdan (talk) 16:52, 4 February 2014 (UTC)

Sure. I also removed it from our article Summation. - DVdm (talk) 17:09, 4 February 2014 (UTC)

So to follow-up on the remark by Tkuvho, the mentioned stuff could be useful to serve as an example at Abel summation.

Thank you - somewhat related (and for those in the know so-to-speak) - made the following userbox =>

${\displaystyle \int \!\,}$

This user knows that ${\displaystyle \sum _{n=1}^{\infty }n=-{\frac {1}{12}}}$ (NYT 2014 reference/archive)

esp ok perhaps if the notion is actually true of course - in any case - Enjoy! :) Drbogdan (talk) 16:17, 5 February 2014 (UTC)

If we are to keep this piece of fluff in the article, it certainly does not belong in the lead. The fact that you can get lots of absurd results by using divergent series is well established, but not very notable. I find that the statement that a technique for assigning a value to a divergent series justifies the result amusing, especially considering that there are many such techniques and they do not all agree. I will move the statement further down in the article, but I don't think it belongs here at all. Bill Cherowitzo (talk) 18:52, 5 February 2014 (UTC)

I agree; it should be removed entirely. It's not about infinity. --Trovatore (talk) 18:59, 5 February 2014 (UTC)

I.m.o. if it belongs anywhere in WIkipedia, perhaps in our article Mathematical fallacy. - DVdm (talk) 19:08, 5 February 2014 (UTC)

I wouldn't go that far, but in any case we don't need to decide it here. Once we're agreed that it's not right for the infinity article, everything else is off-topic. Discussions about how to deal with it in the corpus of math articles generally should go to Wikipedia talk:WikiProject Mathematics. Questions about whether or in what sense it's "true" should go to WP:RD/Math. --Trovatore (talk) 19:29, 5 February 2014 (UTC)

No, it doesn't belong here at all. Sławomir Biały (talk) 01:15, 10 February 2014 (UTC)

The phrase before my edit was as follows: As in the real analysis, in complex analysis the symbol ∞, called "infinity", denotes an unsigned infinite limit. This is plainly wrong: in real analysis the symbol denotes always signed limit.--Reciprocist (talk) 07:22, 18 April 2014 (UTC)

Not always, actually, but I take your point. On the infinity-tilde thing, though, please find it somewhere real, not MathWorld. MathWorld is notorious for making up its own nomenclature and presenting it as though it were standard. --Trovatore (talk) 07:27, 18 April 2014 (UTC)

It's not tilded here, here, here, here, or even here. I tried to find a tilded one, but failed. - DVdm (talk) 08:13, 18 April 2014 (UTC)

We really have to keep an eye out for this MathWorld stuff. Weissstein undeniably performed a service by making a lot of material conveniently available, but that doesn't entitle him to change mathematical usage by sneaky subterfuge. MW may sometimes be a WP:RS for mathematical content (though never an ideal one — we strongly prefer secondary sources to tertiary when available). But it should never be relied on for mathematical usage. Just not trustworthy. --Trovatore (talk) 18:44, 18 April 2014 (UTC)

By the way, what about mentioning directed infinity?--Reciprocist (talk) 05:50, 19 April 2014 (UTC)

Seems to be largely Mathworld only. See Directed infinity and Google Books.- DVdm (talk) 08:19, 19 April 2014 (UTC)

Are you talking about the compactification of the complex plane by adding a circle at infinity, or what exactly? Honestly it's not something I've much come across, but I'm not opposed to adding it if it can be found in RSs. Not sure how much ink it should get, though. --Trovatore (talk) 08:20, 19 April 2014 (UTC)

Shouldn't someone at least mention the point at infinity, which appears so often in physics? (Zero reference for potential fields, location of image for an object at the focus of a concave mirror/convex lens...)121.221.82.88 (talk) 15:07, 15 March 2014 (UTC)

It is a nontrivial problem that the section on physics makes completely unsubstantiated claims. It is almost certainly the opinion of the author and not accepted in physics that there are no infinite physical quantities. The treatment of the singularity is a good example. This is a point with infinite density. It seems the author has a particular aversion to believing in infinity and wishes to project it on the whole of physics. The section on physics needs a drastic rewrite or to be deleted altogether. Without sources, it is an editorial of original opinion and not relevant on wikipedia. — Preceding unsigned comment added by 162.136.192.1 (talk) 14:31, 15 May 2014 (UTC)

Minor issue, but nevertheless...

I had changed the symbol in the lead from "∞" (<big>∞</big>) to "${\displaystyle \infty }$" ("<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)

There should be a very good reason for not using unicode as the mode visible representation. People want to copy and paste this symbol. We should never choose a representation that requires non-default user preferences in order to appear optimal. I do not mind if the Latex is put back in if the unicode symbol is also very prominent - maybe in an infobox, or weaved into the lede somehow. John Vandenberg ^(chat) 10:39, 13 July 2014 (UTC)

Let's have them both, like

Infinity (symbol: ${\displaystyle \infty }$ or ∞) is an abstract concept...

That would put and end to this back and forth changing. DVdm (talk) 11:45, 13 July 2014 (UTC)

By the way, using MathJax, there's not much difference between ∞ and ∞. - DVdm (talk) 11:48, 13 July 2014 (UTC)

I'm cool with the Latex being in there, but I would like it more clearly indicated which is unicode than in your example. John Vandenberg ^(chat) 12:23, 13 July 2014 (UTC)

Perhaps like this?

Infinity (LaTeX symbol: ${\displaystyle \infty }$, Unicode symbol ∞) is an abstract concept...

or

Infinity (symbol: ${\displaystyle \infty }$ in LaTeX, or ∞ in Unicode) is an abstract concept...

I'd prefer the first. - DVdm (talk) 12:44, 13 July 2014 (UTC)

On second thought, I took the latter and went ahead. - DVdm (talk) 08:31, 14 July 2014 (UTC)

Thx. That works for me. John Vandenberg ^(chat) 10:12, 14 July 2014 (UTC)

Not being aware of this discussion, I just changed the opening words of the article to "Infinity (symbol: ∞)", which was promptly reverted with reference to this discussion. I strongly disagree with the current wording "Infinity (symbol: ${\displaystyle \infty }$ in LaTeX, or ∞ in Unicode)". We should always be focused on content, particularly in the lede of an article. The first sentence needs to tell the reader what the symbol for infinity is. The underlying font technology used to display that symbol on the screen is irrelevant. The article could explain somewhere further down how to make an infinity symbol in Latex, or what the Unicode code for the symbol is. These kinds of details are nowhere near important enough to be in the first sentence of the article.

Because the Unicode symbol can be copied and pasted, it should be the sole form presented in the lede sentence. --Srleffler (talk) 18:46, 10 August 2014 (UTC)

I don't see anything in MOS:LEAD that explicitly prohibits what we have here, which, as you can see, was more or less put in place to accommodate the plethora of browser flavours out there. By the way, with my setup, a copy/paste of the Latex symbol results in insertion of the Unicode character "∞", which seems okay. I personally don't care either way, but, apart from your objection, I don't see any compelling problem in keeping both flavours in this case here. In the spirit of wp:consensus trumps MOS, what say others? - DVdm (talk) 07:06, 11 August 2014 (UTC)

I tend to agree with Srleffler. Right now there's too much said about the symbol in the opening sentence. The symbol is not very important.

About the only reason to have the symbol in the opening sentence at all is because people might ask questions if it weren't there. Well, that and the (minor) practical convenience of having a place you know you can copy it from.

So yeah, bottom line, my preference would be to use the Unicode with some sort of markup to keep it from looking so tiny. Second preference would be to defer discussion of the symbol altogether, to later in the article. --Trovatore (talk) 14:07, 11 August 2014 (UTC)

It would be pretty surprising if there were anything in the MOS that explicitly prohibited what we have here, but there is general advice. From WP:LEADSENTENCE there is "Redundancy must be kept to a minimum in the first sentence." Giving the same symbol in both Latex and unicode forms is clearly redundant. It also says "Use the first sentence of the article to provide relevant information...". Telling the reader that one presentation of the symbol uses Latex to render the image and the other uses Unicode conveys no relevant information whatsoever. The font technology used to present the symbol is irrelevant to the topic of the article.--Srleffler (talk) 05:04, 12 August 2014 (UTC)

I agree with Srleffler and others that the emphasis on coding in the lead sentence and the graphic of typefaces at the top is redundant and gives the impression that the symbol and its possible fonts are somehow important to the topic of infinity. --seberle (talk) 16:37, 12 August 2014 (UTC)

I also agree with Srleffler and others, that technical information on how the symbol is rendered is irrelevant and there should only be one symbol in the lead. Don't have much of opinion on which, except that user Trovatore makes a good point; if the Unicode symbol is used, it should be displayed larger. --RacerX¹¹ Talk to me^{Stalk me} 17:36, 12 August 2014 (UTC)

Thx for the comments. Yes, the only reason why we had changed it, was to avoid an eternal switching back and forth between the (good looking) LaTeX ${\displaystyle \infty }$, and the (ugly little) Unicode ∞ version. Is there a way to make it larger other than with the template {{unichar}}? - DVdm (talk) 17:49, 12 August 2014 (UTC)

@DVdm, Racerx11: {{sub|{{resize|250%|∞}}}} yields _∞. I'm not sure if that goes against any MoS or accessibility rules though. The {{sub}} is required because otherwise, the sign starts floating away (∞).—LucasThoms 00:32, 13 August 2014 (UTC)

@DVdm and @Lucas Thoms Thanks for the brief history. I think I am guilty of one who reverted one of those changes. I'm OK with either and _∞ is fine as long it doesn't cause problems. If it boils down to simply aesthetics, I would lean towards ${\displaystyle \infty }$. Btw, I am no expert on markup coding, and although I have a healthy interest in math, I am by no stretch a mathematician. Just adding some input from the outside. I will step back and trust that the participants here will find a good solution. --RacerX¹¹ Talk to me^{Stalk me} 00:59, 13 August 2014 (UTC)

@Lucas Thoms: Nice! So we could open like this:

Infinity (symbol: _∞) is an abstract concept...

Looks perfect to me, and is pure Unicode. - DVdm (talk) 08:31, 13 August 2014 (UTC)

Here's where we run into problems. I'd have to guess that the sub-inside-of-another-sub (_{{sub|...}}) looks great in your browser. In mine (Chrome for Ubuntu and Chrome for Android), one sub puts the symbol in line with the text and two subs puts it too low, halfway below the line of text. —LucasThoms 14:35, 13 August 2014 (UTC)

Firefox here. Just tested in Internet Explorer 8 and 11. Totally different and both pretty bad. Yes, they all think they can design the perfect browser. Amateurism galore. Ah well, free software does come at a price.

The only symbol that seems to consistently render just fine is the LaTeX one, and it can be copy/pasted into a Unicode character for those who want... - DVdm (talk) 15:26, 13 August 2014 (UTC)

Test: This is an infinity symbol: ∞. How does that look? Fundamentally, the difference between the Latex and Unicode representations has nothing to do with Latex or Unicode; it's just that they use different default fonts. We can use Unicode; we just need to specify a font or font family that render better. If the version above doesn't look good in your browser, let me know which browser and give me the name of a font on your system that has a better-looking infinity symbol.

The problem with the symbol "flying away" is because the default font used by Wikipedia on some systems has the symbol floating above the baseline. When you make that bigger, it floats up. The fix for that is not to use that font.--Srleffler (talk) 02:31, 14 August 2014 (UTC)

How about <sub><span style="font-family:serif; font-size: 250%">∞</span></sub>: _∞? That's roughly the size of the LaTeX one everyone liked: ${\displaystyle \infty }$ (this is a little bigger in Chrome, a little smaller in FF). I tested it in Firefox, it's different from Chrome but not necessarily bad. The  are definitely needed for FF, though, or else it starts flying away again. How does that look to those of you with computers that will run IE?—LucasThoms 06:03, 14 August 2014 (UTC)

I'm using FireFox on Windows 8, and the <sub> makes yours sit below the baseline of the text. Trying to make the symbol much larger than the rest of the text is just not going to work, and trying to adjust the position with <sub> is no fix at all, since the positioning of the symbol depends on what font the user is rendering it with.

My default serif font is Times New Roman. What is yours? (See Menu/Options/Content/Advanced) We need to figure out which fonts work and which do not.

How does this look: ∞? This should force Times New Roman if you have it installed, and default serif otherwise.--Srleffler (talk) 06:20, 14 August 2014 (UTC)

That looks perfect to me, Srleffler. --seberle (talk) 10:58, 23 August 2014 (UTC)

In OPERA 12.02 on Hiren's boot CD this show a black rectangle. - 5.23.201.195 (talk) 11:08, 23 August 2014 (UTC)

Pick a font on that system that has an infinity symbol that works. We can cascade fonts as needed to make everyone happy.--Srleffler (talk) 07:50, 24 August 2014 (UTC)

I don't think Hiren's boot CD matters much, as it's kind of a standalone, read-only, stripped down Win XP-system—phew!—, serving as a convenient container for PC maintenance and emergency utilities. It just happens to have an old version of OPERA on board. Picking a font can probably be done by the author of the tool only.

This ∞ looks good on my Firefox, IE8 and IE11—although still slightly floating.

But I still don't see what the problem is with LaTeX ${\displaystyle \infty }$: it is the best looking of them all, and Wikipedia seems to make sure that it copy/pastes to the proper Unicode character on all systems. - DVdm (talk) 09:07, 24 August 2014 (UTC)

It doesn't paste as Unicode for me at all. When I copy/paste the LaTeX symbol, I get "\infty".--Srleffler (talk) 18:13, 24 August 2014 (UTC) If I turn on MathJax, it pastes as Unicode instead. I don't think MathJax is on for users by default, though, so we shouldn't depend on it.--Srleffler (talk) 18:40, 24 August 2014 (UTC)

Sigh. - DVdm (talk) 19:31, 24 August 2014 (UTC)

I found a better solution: ∞. Any comments?--Srleffler (talk) 18:30, 24 August 2014 (UTC)

Looks ok. Translates to <span class="texhtml texhtml-big" style="font-size:150%;">∞</span>. - DVdm (talk) 19:31, 24 August 2014 (UTC)

Looks good to me too. --seberle (talk) 20:02, 24 August 2014 (UTC)

The second paragraph begins, "In mathematics, infinity is often treated as if it were a number." The "often" sounds temporal, as if on one day a mathematician will say that infinity is a number, and then on another day, the same mathematician will contradict herself/himself. Also, that sentence seems to imply that there is a unified mathematics with an authoritative book that spells out all of its rules. The reality is, mathematics is an ever-growing territory with a frontier where future-legendary mathematicians and future-infamous crackpots stake out the boundaries of new formalisms, new algebras, and occasionally whole new branches of mathematics.

It's not sometimes, but in some branches/systems/formalisms of mathematics that "infinity" appears in the names of number-like entities, while in other systems the concept of infinity-as-number simply does not fit in. 129.42.208.184 (talk) 21:28, 23 July 2014 (UTC)

Fair point, but I'm not sure it's too much of a problem at the rather vague level of that sentence. Do you have a suggested alternative wording? --Trovatore (talk) 21:44, 23 July 2014 (UTC)

Actually, the statement is "In mathematics, "infinity" is often incorrectly treated as if it were a number." The word "incorrectly" gives the impression that there is only one correct version of mathematics. Actual infinite numbers are, in fact, used in both complex analysis (as noted in the article) and measure theory. Could we rephrase the sentence as "In elementary mathematics, "infinity" is not regarded as a valid number, but in more advanced marthematics it is useful to augment the number system with infinities."? Or perhaps omit the second clause as it is implied by the first.TerryM--re (talk) 20:48, 10 December 2014 (UTC)

Someone must have added the "incorrectly" reasonably recently. I've removed it. Thanks for pointing it out. --Trovatore (talk) 21:14, 10 December 2014 (UTC)

Update: I found the bad edits, which were on 6 November (this diff), and I have undone them manually (certainly too late to use undo). (My edit summary says "4 november"; sorry about that.) --Trovatore (talk) 21:52, 10 December 2014 (UTC)

I don't like:

${\displaystyle \int _{a}^{b}\,f(t)\ dt\ =\infty }$ means that f(t) does not bound a finite area from ${\displaystyle a}$ to ${\displaystyle b}$

I don't think you can ever correctly write that an integral "equals" infinity. It may sometimes be a convenient shorthand William M. Connolley (talk) 09:24, 11 December 2015 (UTC)

It is quite standard, from the modern perspective of measure theory, to say that certain sets have (for example) a Lebesgue measure that is quite literally equal to ∞. And similarly for the Lebesgue integral, which can be viewed as a sort of generalization of Lebesgue measure. --Trovatore (talk) 09:27, 11 December 2015 (UTC)

The comment(s) below were originally left at Talk:Infinity/CommentsTalk:Infinity/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Last edited at 13:02, 15 April 2007 (UTC). Substituted at 18:55, 29 April 2016 (UTC)

I'm not especially familiar with all this, so perhaps someone else can add Cantor to the history section. He's important enough to be mentioned in the article's introduction (which seems appropriate), so it looks like an oversight to leave him out of the History section. Thanks for considering this! Bob Enyart, Denver KGOV radio host (talk) 19:38, 25 October 2016 (UTC)

I agree. The history section is quite lacking. Aristotle's idea of potential versus actual infinity needs to be carried forward concerning its impact on calculus (potential infinity), how Galileo and Bolzano tried (unsuccessfully) to tackle actual infinity, and (most importantly) how Cantor did develop a successful theory of actual infinity, and its impact on modern mathematics. --seberle (talk) 08:50, 27 October 2016 (UTC)

How much of this is just an issue of section naming/organization? Perhaps "history" should be renamed to "early history" or something? Because the section titled "mathematics" covers a lot of these things. --JBL (talk) 19:00, 27 October 2016 (UTC)

Joel B. Lewis,

There is plenty of explanation on the maintenance tags about the issues. The primary issue is that there is a lot of uncited content in the article. There is also some content in the lead that sounds like original research, rather than a summary of the content in the article.

It's wrong to remove maintenance tags without addressing the issues. It's something to make the article better. Uncited content can be removed.–CaroleHenson (talk) 01:31, 3 April 2017 (UTC)

You have yet to identify a single sentence that you believe to be original research or to need a citation. Do that and then there will be something to talk about. Tagging without actually specifying an issue is worse than useless, and every aspect of your editing on this article so far has been a waste of time. --JBL (talk) 02:32, 3 April 2017 (UTC)

 

Just want to add my voice to Joel's here. Drive-by tagging is useless and should be reverted on sight. Come up with specifics or don't bother. --Trovatore (talk) 05:28, 3 April 2017 (UTC)

And I'll "third" that sentiment. These tags gave me no hint as to what was bothering you about the article. This page is actively watched by many editors and if things were so blatantly wrong that they didn't need to be pointed out, they would have been fixed a long time ago. How am I to know if I have addressed a concern if that concern is not made explicit? --Bill Cherowitzo (talk) 05:55, 3 April 2017 (UTC)

Seriously? This is the first time someone has questioned a refimprove tag. If there's content without citations - that's where citations are needed. Not sure why this so difficult, but I'll start working on the article. It's far easier that having this crazy conversation. There are cn tags already in the article in several places.–CaroleHenson (talk) 09:33, 3 April 2017 (UTC)

I noticed that the article was an "Article for improvement" in May 2013. There was some work on it, but it still had missing citations in early June . There was a Bibliography with a {{more footnotes}} tag on the reference section. I am unclear why the Bibliography section would have been removed. That's better than not having the references at all. Since this is one of the top viewed articles, it would be great to get this in better shape!–CaroleHenson (talk) 10:06, 3 April 2017 (UTC)

Hello fellow Wikipedians,

I have just modified one external link on Infinity. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

• Added archive https://web.archive.org/web/20040910082530/http://www.c3.lanl.gov/mega-math/workbk/infinity/infinity.html to http://www.c3.lanl.gov/mega-math/workbk/infinity/infinity.html

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 14:56, 2 August 2017 (UTC)

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)

The challenge to the work is a figment of imagination. What is the proof that Isha Upnishad is not a mathematical work. What is the proof that infinity is a mathematical concept. Mere ideas and thoughts without valid support cannot be admissible according to wikipedia challenge policies. Please see Wikipedia:Editing policy — Preceding unsigned comment added by Wilkn (talk • contribs) 13:29, 27 August 2017 (UTC)

Kindly stop reverting the article without valid reasons. Please follow Wikipedia:Editing policy, when doing edits. The book by Dr. Sarvapalli RadhaKrishnan is a valid source according to Wikipedia citation sources. Please feel free to remove citations that you feel are not acceptable, but do not remove the whole edit if one of the citations is not acceptable.Wilkn (talk) 13:41, 27 August 2017 (UTC)

Not having valid sources (which most of the information you're adding falls under) is a valid reason for reverting. Moreover, as already pointed out in edit summaries, at the very best you're cherry-picking one translation and generously adding your own interpretations on top of that. This would appear to be in violation of the policy on no original research. --Deacon Vorbis (talk) 13:49, 27 August 2017 (UTC)

Please stop being ignorant. There is no such necessity of distinguishing or arbitrarily defining a work to be mathematical work or philosophical work to understand when a concept originated or how it evolved. The distinction of subjects becomes more clear once they have evolved, not when they are evolving. In India Sanskrit Grammar, idea of Zero, decimal number system all are written in books that are devoted to deities like Shiva etc, formal mathematics started in India with formal numbers and number systems but as part of religious texts (you cannot deny it on lie detector, only deny it using manipulation and only till accepting truth becomes a sign of mental wellness), but you cannot deny these facts claiming that Indians were not writing mathematics. Some people even try to manipulate and wiggle out of their complex by claiming that Upanishads are not philosophical texts but speculative texts, despite tonnes of German philosopher banking on ideas in those Upanishads and rest of modern philosophers banking on those German philosophers. So this wiggling out of complex claiming indian text to be this or that will happen for some more time. We do have Kerala school of mathematics that started calculas 200 years before Newton/Leibniz and eventually people will see reason that some Arab trader must have brought that initial knowledge to europe but for the time being people can safely ignore that part and satisfy their euro-centric complex. Even when India predates something obviously such as in mathematics or philosophy, the biased wikipedia editors from europe/USA will generally write Greek part first, just to help clam their ego. Even when Greeks, Arabs or German themselves will vouch that the idea seems to come from India, the US/UK based editors find it hard to digest. The Isha Upanishad's Poornamidam Shloka uses proper term for infinite that is "absolute/complete", the word infinite in reality is not proper for quantity or number, it is proper only for series, because literal meaning of infinite is one that is not finite or limited, but in reality the number is "complete" in such a way that even when you subtract or add complete to it, it stays the same and the Upanishad defines exactly same properties in just few words in just one shloka how it is complete, by saying that you add anything to it or subtract anything form it, it remains complete, a few more things. You cannot respect intellect without having both honesty (truthfulness) and level of intellect you are observing. In fact being truthful is a prerequisite to being intellectual, you are only as intelligent as you can truthfully represent, the moment you stop representing truths as they are, your intellect has fallen short. This extraordinary note of mine I am copy pasting, so if needed I can add it back here. But feel free to wiggle out of complex by removing it if you want, I will come sometime later and add it here. — Preceding unsigned comment added by Skant71 (talk • contribs) 2:02 pm, Today (UTC−4)

User:Skant71 - Please read the civility policy. Your comment above, "Please stop being ignorant." is hostile. Please be polite. Robert McClenon (talk) 16:13, 27 August 2017 (UTC)

I second and fully and strongly support the sentiments and arguments that are offered in the "Reply to Isha Upanishad Quote." Thank you sir for your valuable comments. I tried to add the sholok myself, but it was reverted by another biased editor. Please see our conversation about infinity in the link - https://en.wikipedia.org/wiki/User_talk:Wcherowi#Infinity — Preceding unsigned comment added by Wilkn (talk • contribs) 16:58, 26 August 2017 (UTC)

User:Wilkn - Please read the civility policy. Saying that another editor is "biased" is not helpful. Robert McClenon (talk) 16:13, 27 August 2017 (UTC)

Kindly respond before making any reverts. — Preceding unsigned comment added by Wilkn (talk • contribs) 13:31, 27 August 2017 (UTC)

Please be civil and provide reliable sources for edits, and discuss any additions here rather than edit-warring. While moderated discussion at the dispute resolution noticeboard is a reasonable way to resolve this, it should only be used if discussion here is inconclusive. Try discussing here for at least 24 hours. Robert McClenon (talk) 16:19, 27 August 2017 (UTC)

This edit request has been answered. Set the |answered= parameter to no to reactivate your request.

In the Indian civilization, one of the mantras of Brihadaranyaka Upanishad and Ishavasya Upanishad popularly known as Shanti Mantra, around 700 BCE talks about the concept of infinity. The mantra is mathematical-philosophical introduction to the concept of infinity. It 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 infinite. "This" is infinite. Infinite comes from Infinite. Take infinite away from infinite, the remainder is infinite." ^[1]. Here the root word, poorna = infinite. Other interpretations of the word, 'poorna' is are full and perfect ^{[2] [3] [4]}.

 Not done Request does not reflect consensus. --Deacon Vorbis (talk) 17:58, 1 September 2017 (UTC)