Talk:Infinity

Achilles v. Tortoise race duration

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

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

$10{\frac {10}{99}}={\frac {100}{99}}=1.010101...$ not $10.101010...$ Oh, you do not mean a multiplication, but the vulgar fraction $10{\tfrac {10}{99}}$. 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)

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

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)

History section - Dubious Tag Discussion

In the pages History section the Brihadaranyaka Upanishad is cited as showing how ancient Indians understood the concept of mathematical infinity. I found no such support for this claim given in the English translation for this and instead it only refers to infinite from a spiritual sense, not specifically within the context of an abstract mathematical or philosophical concept. I don’t claim to be familiar with this source but if we do keep this source it would follow we must also discuss all other ancient cultures who made reference to the idea of the eternal or everlasting as equally being aware of the idea of infinity.

Perhaps we need to better define whether we are covering the history of mathematical infinity or infinity in a broader perhaps more spiritual sense. This way we can narrow down what should and should not be included in this section. 121.98.205.163 (talk) 06:34, 14 September 2022 (UTC)

I thought that looked familiar. That section is very similar to what was discussed here, which ultimately (IMO as a participant in that discussion) ended in a consensus to not include the text, and with the OP receiving an indefinite block which is still in place. Looks like it was re-added in February, but with no better sourcing than before, so I've re-removed it. Writ Keeper ⚇♔ 13:59, 14 September 2022 (UTC)

"Taylor Archibald" listed at Redirects for discussion

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)

that which is

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)

@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)

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)

@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)

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)

@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)

"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)

exacting and ultra-exacting cardinals

"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)

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)

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