Talk:Infinity

@D.Lazard: We are in agreement that Achilles takes ${\displaystyle {\frac {10}{0.99}}}${\displaystyle {\frac {10}{0.99}}} seconds to overtake the tortoise. As a repeating decimal, that's 10.101010... seconds. You claim that this is ${\displaystyle 10{\frac {100}{99}}}${\displaystyle 10{\frac {100}{99}}} seconds, but that works out to 11.010101... seconds. My replacement, ${\displaystyle 10{\frac {10}{99}}}${\displaystyle 10{\frac {10}{99}}} yields 10.101010..., which is what we want.

Peter Brown (talk) 02:23, 23 July 2021 (UTC) [reply ]

${\displaystyle 10{\frac {10}{99}}={\frac {100}{99}}=1.010101...}${\displaystyle 10{\frac {10}{99}}={\frac {100}{99}}=1.010101...} not ${\displaystyle 10.101010...}${\displaystyle 10.101010...} Oh, you do not mean a multiplication, but the vulgar fraction ${\displaystyle 10{\tfrac {10}{99}}}${\displaystyle 10{\tfrac {10}{99}}}. IMO, even correctly formatted, this must be avoided, as vulgar fractions are not commonly used in many countries. I'll add a multiplication sign. D.Lazard (talk) 08:20, 23 July 2021 (UTC) [reply ]

Yes, I was interpreting ${\displaystyle 10{\tfrac {10}{99}}}${\displaystyle 10{\tfrac {10}{99}}} as a mixed number. Now, it isn't obvious to me, or probably to the general reader, why ${\displaystyle {\frac {10}{1-0.01}}}${\displaystyle {\frac {10}{1-0.01}}} should be equal to ${\displaystyle 10\times {\frac {100}{99}}}${\displaystyle 10\times {\frac {100}{99}}} or why anyone should care. I am accordingly omitting this step. Peter Brown (talk) 18:15, 23 July 2021 (UTC) [reply ]

I am not persuaded that this mathematician solved Zeno's paradox in 1821. At minimum I recommend editing this to say that he claimed to solve the paradox. First, the only citation is to an original document in French. If this mathematician really did solve Zeno's famous paradox, an English citation or description of the work to show that it has stood up to peer review would be more persuasive. Second, and perhaps more compellingly, how does a repeating value solve a paradox that is primarily concerned with the problem of infinite regression? On the face of it, this does not seem to offer a solution to the paradox, but only supports the challenge/dilemma of the paradox further. Empiric78 (talk) 13:39, 9 October 2024 (UTC) [reply ]

The redirect Taylor Archibald has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2023 July 13 § Taylor Archibald until a consensus is reached. —Lights and freedom (talk ~ contribs) 07:52, 13 July 2023 (UTC) [reply ]

In this edit, Panamitsu changed "...that which is..." to "...something which is..." in the first sentence.

I think I understand the concern — that which is could be seen as excessively flowery or old-fashioned. But something which is does not strike me as an entirely adequate replacement, for a couple of reasons:

• First, I know this is a bit of an American preoccupation, but it ought to be something that is if anything
• More seriously, the reader is tempted to view this "something" as referring to some specific thing, and that is not what the article is about

Lacking a better suggestion, I would prefer to restore that which is, which is not that exotic and which fairly elegantly solves the specificity problem. But maybe we can come up with a third option which is ha, I did it myself better still? --Trovatore (talk) 19:20, 8 August 2023 (UTC) [reply ]

@Trovatore Oh, sure, I'm just a bit confused about your concern about the article not being about a specific thing. Are you able to elaborate? In my mind, endless or infinite can only be used to describe something (whatever that may be), and that "something" in the article says "an arbitrary thing." Just like how the Oxford dictionary defines it as "a thing that is unspecified or unknown." Panamitsu (talk) 21:13, 8 August 2023 (UTC) [reply ]

My intuition is that this "something" can be read in two ways — it could be a "generic" something, or it could be some particular thing the speaker already has in mind (that would still be "arbitrary" in the sense that the word places no restriction on what the speaker might have in mind). For that reason I still like that which is better. --Trovatore (talk) 21:21, 8 August 2023 (UTC) [reply ]

@Trovatore I disagree about your point about the reader already having something in mind, considering that it is at the start of the article. Pulling from the Oxford dictionary, how about we use something similar to "the quality of being endless"? Panamitsu (talk) 08:30, 9 August 2023 (UTC) [reply ]

No, not the reader; the writer. It's like if I say "I have something to tell you". What you hear is that I have something specific already in mind, not that I just want to speak. So it could be interpreted as "there's this thing called infinity, and now I'm going to tell you some particular things about it, namely that it's boundless etc".

"Quality" seems to point too much away from interpretations that are objects (not that qualities can't be objects, but it's not what you think of).

What's really wrong with that which is? I thought it was kind of a nice solution. --Trovatore (talk) 16:04, 9 August 2023 (UTC) [reply ]

@Trovatore I've personally never heard of "that which is" before, so it doesn't seem to make sense to me. Perhaps it's a technical term that I just haven't been exposed to. Panamitsu (talk) 22:34, 9 August 2023 (UTC) [reply ]

"That which is" sounds perfectly fine to me, and is a common expression. Also, I don't think "something" is likely to be misunderstood in this context at the beginning of the article, though it does sound a bit awkward. Both solutions sound acceptable to me, though I prefer "that which is". seberle (talk) 10:55, 10 August 2023 (UTC) [reply ]

"The discovery of exacting and ultra-exacting cardinals represents a significant advancement in set theory and large cardinal theory."

https://www.popularmechanics.com/science/math/a63121596/exacting-cardinal-infinities/

https://www.newscientist.com/article/2459158-mathematicians-have-discovered-a-mind-blowing-new-kind-of-infinity/

https://arxiv.org/pdf/2411.11568

Juan Aguilera, a co-author of the paper from Vienna University of Technology

69.181.17.113 (talk) 02:09, 13 December 2024 (UTC) [reply ]

I would suggest starting with the large cardinal page rather than here. This article should probably mention large cardinals at a high level (which currently it doesn't seem to), but not get into too much detail. --Trovatore (talk) 02:16, 13 December 2024 (UTC) [reply ]

Agreed on both. - CRGreathouse (t | c) 15:47, 13 December 2024 (UTC) [reply ]

I'm still trying to figure out if I think the image of the Sierpiński triangle is a good idea. I have to admit I can't think of anything better off the top of my head. It's certainly better than just an image of the symbol, and probably better than at least the current image of the reflecting mirrors, which I think is visually kind of confusing and noisy.

But in any case I copyedited the caption. I don't know what it means for something to "contain an infinite amount of itself". I tried to replace it with something meaningful and accurate; not sure if it's too wordy. --Trovatore (talk) 19:30, 16 January 2025 (UTC) [reply ]

I think the Sierpiński triangle is a good image here, and I think your text is fine. Personally I'd scrub the "because of its recursive pattern" to keep it snappy but I don't mind the current version. - CRGreathouse (t | c) 02:42, 17 January 2025 (UTC) [reply ]

Yeah, I considered that. With your encouragement I'll go ahead and kill it. --Trovatore (talk) 02:45, 17 January 2025 (UTC) [reply ]

We could use its animated GIF or another fractal zoom GIF which I think makes the recursion a lot more self-evident if that is the way we want to go, but in my opinion having a vanishing point image like File:Ambigram tessellation Milan - concentric circles.png portrays it very well without being overly distracting. It would work great for the printable version of the article too. I'd be against using any real-world example like the last image because there are none that truly exist. --– Mullafacation {◌͜◌ talk} 19:20, 18 January 2025 (UTC) [reply ]

I'm not a huge fan of animations in articles, but there's something to be said for the Sierpiński zoom. Could we make it sub in the static version for printable?

For the Milan thing, to be honest, I'm not sure what I'm looking at there.

As to whether there are any "that truly exist", that's sort of an open question. I've kind of toyed around in my head with the image at right (read the caption). I'm sure we could find a prettier one if we wanted to go that way. But the main thrust of this article seems to be mathematical rather than physical, so I kind of think probably not, but it's worth throwing out there. --Trovatore (talk) 19:45, 18 January 2025 (UTC) [reply ]

If we go with the animated GIF, the printable version will be the first frame which looks the same as the image we have. And there's nothing special about the Milan image, it just looks like a tunnel with no ending. The pi image does the same thing but it is also serves as a practical mathematical example so I would prefer that. I did see in the article that it's an open question about the universe but I meant we can't show a picture that truly shows the infinity of anything in the real world. If it's an open question, it's not the strongest example we can choose. I don't know if there's any examples of images that suggest that the universe might be infinite but the image there doesn't. With pi there's no obvious reason why it's infinite while with the Sierpiński triangle you can see by looking at it how it is able to fit inside itself and go on forever. – Mullafacation {◌͜◌ talk} 21:54, 18 January 2025 (UTC) [reply ]

OK, I'm on board with something like the Sierpiński animation, but I would prefer higher resolution and maybe a little pause on the first frame. Right now it kind of looks "off-balance" as it immediately descends into a non-centered part of the image. I wonder if someone has come up with an animated version of SVG? --Trovatore (talk) 22:10, 18 January 2025 (UTC) [reply ]

I do not think that the Sierpiński triangle ia a good first image, because the reader must have a rather good knowledge of infinity to understand where is the infinity of this image. IMO, this image is much more pedagogical:

D.Lazard (talk) 20:17, 18 January 2025 (UTC) [reply ]

I think that's too symbolic, too text-based for my liking. The Sierpiński image at least moves away from symbolic representation.

We could also consider the zero option. When it's too hard to find an appropriate image, it's worth thinking about whether an image is really needed. Shoving in images purely pro-forma doesn't appeal to me.

That said, I do think the Sierpiński triangle is better than nothing, and I also prefer it to the decimal representation of π. --Trovatore (talk) 20:41, 18 January 2025 (UTC) [reply ]

I agree. I don't like putting the decimal approximation of pi. There are already too many people that have the misunderstanding that "pi is infinite." seberle (talk) 23:21, 20 January 2025 (UTC) [reply ]

• C-Class level-3 vital articles
• Wikipedia level-3 vital articles in Mathematics
• C-Class vital articles in Mathematics
• C-Class Philosophy articles
• High-importance Philosophy articles
• C-Class logic articles
• High-importance logic articles
• Logic task force articles
• C-Class mathematics articles
• Top-priority mathematics articles
• Wikipedia former articles for improvement

• All Wikipedia vital articles