Talk:Infinity symbol

Tipped Hourglass
Represents time no longer flowing/running out. — Preceding unsigned comment added by 47.55.176.9 (talk) 20:08, 9 January 2015 (UTC)
 * You have a reliable source for this interpretation? —David Eppstein (talk) 21:18, 9 January 2015 (UTC)
 * symbolsage.com/eternity-symbols-and-meaning/ octavia
 * Does not mention hourglasses. And what evidence is there that this web site meets Wikipedia's standards for reliability? —David Eppstein (talk) 05:44, 26 September 2021 (UTC)
 * In familiy trees the 90 degree rotated 8 is used to indicate 'marriage'. Sorry, maybe I am just the kind of person that needs to be told that the letter 'a' means 'the letter 'a' '. — Preceding unsigned comment added by 2A0A:A549:7055:0:ED7F:25C5:A476:330D (talk) 05:41, 13 April 2023 (UTC)

Origin?

 * Perhaps whoever invented it was considerate for typesetters and chose a form that could be typeset easily as an 8 on its side ("lazy 8"). Anthony Appleyard (talk) 07:38, 22 November 2015 (UTC)
 * Ok, but why 8 rather than any other symbol that looks different tipped sideways? And have you looked at the original printing of Wallis, as reproduced online? It doesn't seem that he was trying to be kind to typesetters in other ways. Anyway, we should be using reliable sources here rather than speculating ourselves. —David Eppstein (talk) 07:51, 22 November 2015 (UTC)

Graphic Design
The Infiniti logo is not a deformed version of the infinity symbol, it's clearly a road pointing in the distance, such as this image http://i.imgur.com/spCswXb.jpg. Don't see the point of including this obscure Lazy 8 studios, given that there are plenty of other more notable examples without it, and their Wikipedia page doesn't even show the logo. It isn't supposed to be an exhaustive list of companies employing the infinity symbol in their logo. CrocodilesAreForWimps (talk) 04:22, 15 July 2016 (UTC)
 * I don't see why the Infiniti logo can't be both a deformed infinity symbol and an image of a road leading to infinity, at the same time, a visual pun. But since this is obviously contentious, we need reliable sources and all I can find are unreliable and contradictory web sites and discussion forums. Unless someone can find sources, we're better off without this; it's not needed to make the point that the symbol is a frequent subject of logo design. —David Eppstein (talk) 06:25, 15 July 2016 (UTC)
 * Doesn't make sense to look at it as a deformed ∞, when there's a very obvious meaning in it that conveys the concept of infinity in the context of driving. If other people have the opinion it can be interpreted differently that's nice, but it has no place without a reliable source, as you say. CrocodilesAreForWimps (talk) 19:02, 15 July 2016 (UTC)
 * This source appears to be reliable, and confirms that the symbol has more than one meaning. But the two meanings it gives are the road one and Mt. Fuji, not the infinity symbol. —David Eppstein (talk) 20:19, 15 July 2016 (UTC)

Removed unreferenced statement about rotating an "8" by 90 degrees
This unreferenced statement is most likely false. Please read the section Typesetting 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.

In 2011, I removed a similar sentence from Infinity. For the 2011 reply to my above statement, see Talk:Infinity. --RJGray (talk) 16:13, 6 September 2017 (UTC)
 * Actually, the cast metal letters and symbols were rectangles or squares of various sizes, the illustration in Typesetting is just an example. And the pages of some mathematical journals were composed manually until very recently in some countries (in India for instance; I have under the eyes a reprint from the Indian Journal of mathematics (Allahabad) of 1990, in which it is clearly the case; it is quite a work of art!). So it is perfectly possible that some symbols were sometimes rotated. But I agree that it would need to be sourced. Sapphorain (talk) 17:15, 6 September 2017 (UTC)

Utter nonsense
The first sentence of the Usage sentence is as follows:

"''In mathematics, the infinity symbol is used more often to represent a potential infinity, rather than an actually infinite quantity as included in the extended real numbers, the ordinal numbers and the cardinal numbers (which use other notations). For instance, in mathematical expressions with summations and limits such as the one below:
 * $$ \sum_{n=0}^{\infty} \frac{1}{2^n} = \lim_{x\to\infty}\frac{2^x-1}{2^{x-1}} = 2,$$

the infinity sign is conventionally interpreted as meaning that the variable grows arbitrarily large towards infinity—rather than actually taking an infinite value.''"

This is complete nonsense.

There is no such things as a "potential infinity" in mathematics.

The infinity symbol as the upper limit of the summation sign signifies an actual infinity: the number of terms in the summation.

Nonexistent concepts such as "potential infinity" do not need to be invented and cited. 2601:200:C000:1A0:A092:B45C:E058:ACB4 (talk) 00:37, 3 November 2021 (UTC)
 * Potential infinity is a well-studied concept, not one invented recently. However, I'd like instead to pick out a very serious error in your comment. The upper limit of a summation sign does not conventionally denote the number of terms in a summation; when finite, it denotes the largest term. When written as the infinity symbol, it does not denote the fact that there are infinitely many terms, but rather the fact that there is no largest term. The summation is not taken to include an infinite term, in such cases. —David Eppstein (talk) 01:17, 3 November 2021 (UTC)

Euler's variant
I restored the mention of Euler’s variant of Wallis symbol’s of infinity. I think the mention of it is relevant to this page, and especially so since Euler is very famous. The fact that we don’t have secondary sources confirming this variant didn’t catch on appears to me as a further argument to mention it, as the primary sources (Euler’s papers), are a proof it was indeed used. Wikipedia cannot restrain from using information on the ground that it is not confirmed by a secondary source: it would mean Wikipedia is a second rate encyclopedia.--Sapphorain (talk) 20:50, 4 January 2022 (UTC)
 * User:Sapphorain has now twice reverted my removal of the material claiming that Euler used a variant of this symbol, adding off-topic material about Euler's use of the mathematical concept of infinity rather than of this symbol specifically, separately claiming that this variation was not used by anyone else, and separately claiming that this variant resembles a totally-unrelated symbol in Unicode for something in Japanese, sourced only to Euler's own works. The material does not contain any secondary sources attesting to the significance of this variation in the history of the symbol. It does not have sources backing up the implication that this was a deliberate and significant change to the symbol rather than just a minor typographic variant, much like different fonts with this symbol today vary in having constant or variable line width, equal or unequal lobe size, and broken or unbroken lines at the crossing point. And it does not have sources proposing the vaguely-similar Japanese symbol as a way to display something resembling Euler's symbol. I am trying to get the article in shape for a Good Article nomination and Sapphorain's insistance on including unsourced original research is a significant obstacle to this effort. Does anyone besides Sapphorain think it should be there? Alternatively, can any of this material be properly sourced? —David Eppstein (talk) 20:56, 4 January 2022 (UTC)
 * I just wish to mention here, for the sake of precision, that User:David Eppstein has now twice reverted my original inclusion of the mention of Euler's variant. I will of course respect a consensus on that matter.--Sapphorain (talk) 21:11, 4 January 2022 (UTC)
 * Since you mention precision, you are being incorrect and imprecise. I did not twice revert your edit. I removed your material once, not as a specific revert of its addition, but as part of a much larger effort to revise the article and clean out cruft from it. In doing so I did not look at the edit history and did not pay any attention to when it was added, who added it, or whether it was added in a single edit. I then reverted your re-addition of the material, once. —David Eppstein (talk) 21:17, 4 January 2022 (UTC)
 * I agree with David's removal of the text written by Sapphorain: it is not only poorly sourced, but also contains considerations on Euler's views of infinity, that do not belong to this article, even if they were correctly sourced. However, the figure could be restored with a caption such as "typographic variant of the symbol that was used by Euler". D.Lazard (talk) 21:23, 4 January 2022 (UTC)
 * Well, maybe, if it were a totally different image that actually looked like Euler's symbol, if it fit among all the other images in the article, and if we had sources documenting whether it was intended as a variant, the same symbol just looking different because of how it was typeset, or a different symbol altogether. I'd rather find a way of squeezing in the Métis flag. —David Eppstein (talk) 22:41, 4 January 2022 (UTC)

I had never heard of this variation of the symbol before, but Cajori, A History Of Mathematical Notations Volume II §421 does talk about it, in one sentence. So I guess it's reasonable to mention it in an article about the symbol, without over-emphasizing it. (By the way, there's some other interesting stuff in that section too, like the notation $$\infty^n$$, which I see was discussed at MathOverflow before.) Adumbrativus (talk) 02:29, 5 January 2022 (UTC)
 * I agree completely with David Eppstein's criticism of Sapphorain's edit. But based on this Cajori source, I also agree with Adumbrativus that it would be perfectly reasonable to replace Sapphorain's three sentences by a single one along the lines of something like "Various mathematicians, including Leonhard Euler, have used certain typographical variants of the symbol, particularly an open version." But it would also be fine to remove altogether. Gumshoe2 (talk) 03:01, 5 January 2022 (UTC)
 * So first let me say thank you to Sapphorain and Adumbrativus for the delightful links! I guess the Cajori one is in the public domain?  And the original Euler piece had some very enjoyable stuff:  Expressiones ergo $$\frac{2\cdot3\cdot7\cdot11\cdot13\cdot \mathit{etc}}{1\cdot2\cdot6\cdot10\cdot12\cdot\mathit{etc}}$$ valor est infinitus, et posito absolute infinito $$=\infty$$, erit istius expressionis valor $$=l\infty$$, quod infinitum inter omnes infiniti potestates est minimum. (Here I've used the ordinary &infin; because I don't have the variant handy.) I guess the $$l\,\!$$ means logarithm, and the point is that the infinite product diverges very slowly?  But why is it the smallest?  Wouldn't the double logarithm be smaller, looking at things this way?
 * Anyway, neither here nor there. David is quite right that we shouldn't be inferring something like this from a possibly oddly typeset primary source.  But now that there's a secondary source, I think it would be nice to mention it.  Not everything we do has to be grim and serious. --Trovatore (talk) 07:06, 5 January 2022 (UTC)
 * My guess at the terminology is that "$=l$" means "equals in the limit". He seems more careful to distinguish this from the usual kind of equality than I might have supposed, given the stereotype of his sloppy manipulations of series. —David Eppstein (talk) 08:35, 5 January 2022 (UTC)
 * Hmm, but then why would he say that it's the smallest infinite among all infinite powers? --Trovatore (talk) 16:24, 5 January 2022 (UTC)
 * Euler's paper has an English version.--SilverMatsu (talk) 15:04, 5 January 2022 (UTC)
 * Maybe, but you don't seem to have linked to it :-). In any case the Latin seems quite readable. --Trovatore (talk) 16:25, 5 January 2022 (UTC)
 * Sorry, the correct link is this(PDF). The link I wrote earlier was the original Latin version.--SilverMatsu (talk) 00:39, 6 January 2022 (UTC)

Usage in mathematics
@David Eppstein, I have a question regarding these series and limit expression in this section. I couldn't find any relation between this expression
 * $$ \sum_{n=0}^\infty \frac{1}{2^n} = \lim_{x \to \infty} \frac{2^x - 1}{2^{x-1}} = 2 $$

Also, I haven't found yet that expression in a cited reference, especially for that limit. Would you like to give an explanation? Regards, Dedhert.Jr (talk) 10:26, 17 August 2022 (UTC)
 * This article is not about the truth of these equalities, but about their use of $$\infty.$$ Nevertheless, the fact that the sum of the series is 2 is proved in geometric series and 1/2 + 1/4 + 1/8 + 1/16 + ⋯. The value of the limit results from the equality $\frac{2^x - 1}{2^{x-1}}=2-\frac 1{2^{x-1}}$ and the basic properties of exponential function. D.Lazard (talk) 13:26, 17 August 2022 (UTC)
 * Yes, pretty much. The limit is of partial sums of the series. They were chosen merely to display the notation rather than to have any deep mathematical significance. I think WP:CALC allows us to include such material without requiring a source. —David Eppstein (talk) 16:05, 17 August 2022 (UTC)

How to type ∞?
Tap the ?123 button and tap =\< button and go to the = and hold it for 3 sec and go to 1 left and you can type infinity method: 2 type ∞ in the google search and go find the symbol in the text blue it and tap copy and go to your keyboard and tap the text thing for 0.0167-1 sec and tap paste and ∞ method 3: go to settings and go to symbols and insert =(but holded and holded 1 left) and type in the name the name of the symbold and go to keyboard and type somthing you named it and it will apper and this won't update i will just let you guys enjoy and those are just the 3 methods to type it 2601:680:8301:73E0:94BC:EB38:87BF:6E05 (talk) 06:14, 2 January 2024 (UTC)


 * Or you could get a Mac and just hold down the option key while typing 5. ∞. —David Eppstein (talk) 06:47, 2 January 2024 (UTC)
 * I have no idea how to type that symbol, so maybe you could just literally copy-and-paste it? But meh! Whatever! Dedhert.Jr (talk) 07:38, 2 January 2024 (UTC)
 * A tip for phones 2601:680:8300:3870:D810:567:A288:3C99 (talk) 18:13, 8 January 2024 (UTC)