Talk:Infinity (disambiguation)

Infinity puzzle

Anyone remember the "Infinity" jigsaw-type puzzle that came out in the 1990s? Any chance of an entry about it? --Bonalaw 09:40, 17 March 2006 (UTC)

Infinity Game series

It's worth mentioning that the link for the Infinity game series, (presumably referring to those written by Kotaro Uchikoshi, incorrectly links to the composer Per Nørgård, which is completely unrelated, and needs fixing. Wanyal1 (talk) 18:40, 2 July 2015 (UTC)

Description of Infinity

An edit war is starting with Bkonrad, who insists for describing the content of the linked article as "something without any bound". This phrase appears in the linked article, but is completed by "or something larger than any natural number". Together, these two phrases are not a definition of the concept, but an introduction to the remainder of the lead. So, even with the second phrase added, this is not an accurate description of the subject of the article.

Also, while all the article is about the mathematical concept and its applications in sciences. Even the section "Arts, games, and cognitive sciences" is about applications of the mathematical concept.

Also, the phrase "something without any bound" is a dictionary definition of the common meaning of the word. It does not indicates that most of the linked article is about mathematics.

So I have edited the article for beginning it with Infinity is a scientific concept. Probably "a mathematical concept" would be better, and this deserve a discussion.

These are the reasons of my edit. In summary it consists of applying WP:LEAST. Please, discuss on the best formulation in view of WP:CONSENSUS. D.Lazard (talk) 16:23, 27 October 2019 (UTC)

Starting with Infinity is a mathematical concept... seems appropriate. However, it also should be described in some way. — MarkH21 (talk) 17:51, 27 October 2019 (UTC)

Note that I only replaced the inadequate description "is a scientific concept" that had been insisted upon by D.Lazard with language taken directly from the lead sentence of the article. FWIW, "is a mathematical concept" is better than "is a scientific concept". Yet there is no expectation that the description provided on a disambiguation page is a complete definition, especially when the entry is a highly complex topic like infinity. The point is to provide enough context for a reader to know which entry on the disambiguation page to select. Since infinity is the primary topic and many readers will have arrived at the disambiguation page from the primary topic, a vacuous formulation such as "is a mathematical concept" is likely adequate. However, if this were not the primary topic, I think some brief substantive description such as "something without any bound" would be more helpful for readers. I'm not sure the additional qualification "or something larger than any natural number" offers any meaningful distinction for most readers. older ≠ wiser 18:15, 27 October 2019 (UTC)

Well, unboundedness is certainly not the relevant feature. There are infinitely many natural numbers, but they're bounded below by zero and above by ℵ₀ or ω depending on whether they’re considered as cardinals or ordinals. Let's go with "mathematical concept". Peter Brown (talk) 18:51, 27 October 2019 (UTC)

There are bounds and then there are bounds. ℵ₀ or &omega are boundaries in a highly abstract technical sense. I mean seriously, it's like saying the infinite set of natural numbers is bound by this other infinite set. Certainly it is meaningful for some applications, but for most people boundless is a useful shorthand. older ≠ wiser 19:13, 27 October 2019 (UTC)

For most people the term "boundless" means vast, immense. Check out the sample uses of the term here—a tiny proportion actually involve the infinite. Melville's use in Moby-Dick, Chapter LXIV, is more typical:

Seems it not but a mad idea, this: that in the broad boundless ocean, one solitary whale, even if encountered, should be thought capable of individual recognition from his hunter.

Peter Brown (talk) 20:09, 27 October 2019 (UTC)

In mathematics, one encounters often sentences like "there are infinitely many real numbers x such that 0 ≤ x ≤ 1." Unboundness is wrong here, as this set of numbers is bounded below by zero and above by one. So the description of the linked article as "something without any bound" is definitively misleading. Moreover, it is also confusing, as not distinguishing between a dictionary definition of the common meaning of the word from the subject of the article. D.Lazard (talk) 14:36, 28 October 2019 (UTC)

Bkonrad allows, above, that "a vacuous formulation such as 'is a mathematical concept' is likely adequate." He/she is willing, it seems, to forgo the reference to bounds that D.Lazard and I have opposed. Our opposition, however, should also extend to the lead sentence in the Infinity article itself. It also mentions bounds, and the vacuous formulation violates MOS:CONTEXTLINK as well as other requirements for a lead sentence. How do we meet these needs? Peter Brown (talk) 17:15, 28 October 2019 (UTC)

I agree that both the dab page and the target article must be edited. For the dab page, Infinity is a mathematical concept is ok for me. If we want to be more descriptive, one can expand this as Infinity is a mathematical concept that is involved in almost all branches of mathematics, and used in many scientific and non-scientific areas. The wording can probably be improved, but this describes accurately the content of the article.

For the article, not only the first sentence must be changed, but the whole first pragraph deserves to be rewritten. The first sentence can be kept if preceded by "In common language". This could give something like In common language, infinity describes something without any bound, or something larger than any number. During centuries, the nature of the infinity was the subject of many discussions among philosophers (see infinity (philosophy)). Mathematicians began to work with infinitely small and infinitely large quantities, with the introduction of infinitesimal calculus. At the end of 19th century AD, Georg Cantor introduced and studied infinite sets and infinite numbers, which can be of various sizes. This makes infinity a mathematical concept that can be studied, manipulated and used in the same way as any other mathematical object. This is only a draft, which can certainly be improved, but I think that such a presentation is the best way for avoiding misunderstanding. D.Lazard (talk) 20:39, 28 October 2019 (UTC)

Excellent!! Initial criticisms:

• without any bound

Is "bound" as a noun "accessible" to a lay audience, per MOS:LEAD? It's much used as a verb: "bound for Australia", "bound by my contract", etc. The phrase "out of bounds" is familiar enough, but it doesn't use quite the same word. Outside of mathematical contexts, the use that comes to mind is

As I drew in my head, and was turning around,
Down the chimney St. Nicholas came with a bound.

But that's from a poem nearly 200 years old and anyhow it uses the wrong sense of the word.

• During centuries

Everything that happens happens during centuries. Perhaps you mean "for centuries"?

• the nature of the infinity

The definite article implies that there is only one infinity. Is that intended?

• Mathematicians began to work with infinitely small and infinitely large quantities

Newton was careful to avoid reference to what Berkeley called "Ghosts of departed quantities". Perhaps Leibniz thought that he was working with infinitely small quantities; I'm weak on this bit of history. Anyhow, since Cauchy's clarification of the limit concept, we know that what was valuable in the project didn't really involve quantities like that.

Who have you in mind who worked with infinitely large quantities? Thomas Digges, perhaps?

• in the same way as any other mathematical object

So infinity is a mathematical object? I think that the infinity of prime numbers differs from, e.g., the infinity of complex numbers with absolute value less than 1; they are not the same mathematical object. You may disagree. Perhaps infinity is a quality, not an object.

Carry on! Peter Brown (talk) 22:22, 28 October 2019 (UTC)

By the way, though WP:TPO advises that one "not break up another editor's text by interleaving your own replies to individual points," I have NO objection whatever if you should choose to do so. Just use a clearly different font or color. Probably not red or green, in deference to readers with a red/green visual deficiency. I've been scolded for such interleaving myself, but it is sometimes appropriate. Follow common sense, as {{subcat guideline}} notes. Peter Brown (talk) 04:16, 29 October 2019 (UTC)

"Infinity (audio)" listed at Redirects for discussion

A discussion is taking place to address the redirect Infinity (audio). The discussion will occur at Wikipedia:Redirects for discussion/Log/2021 October 25#Infinity (audio) until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 64.229.90.53 (talk) 04:27, 25 October 2021 (UTC)