Talk:Infinite monkey theorem

Monkey caption

Previously, the caption said "A Chimpanzee probably not writing Hamlet." This was funny, but perhaps too humorous for an article. A user opted to change it to "a chimpanzee sitting at a typewriter," which, although changing the caption is reasonable, strikes me as redundant. Worth changing to something else? Delukiel (talk) 13:09, 21 October 2023 (UTC)

I changed it to "A chimpanzee typing random characters", which seems to capture both the sense of the image and the article. — Loadmaster (talk) 16:39, 22 October 2023 (UTC)

Works for me! Delukiel (talk) 00:35, 24 October 2023 (UTC)

This was discussed (briefly) in talk:Infinite monkey theorem/Archive 4#probably not. I still think it's fine to have it. It's a little bit The Economist-style, but I don't think it outrages the encyclopedic form. --Trovatore (talk) 00:51, 24 October 2023 (UTC)

Either one works for me (admittedly, I prefer the original, but I love goofball captions), I just thought what it was changed to was redundant. Delukiel (talk) 01:12, 24 October 2023 (UTC)

+1 for the original, it really doesn't hurt anyone. Dialmayo (talk) (Contribs) she/her 11:21, 24 October 2023 (UTC)

I've changed it back to the original. Delukiel (talk) 06:34, 26 October 2023 (UTC)

:D Dialmayo (talk) (Contribs) she/her 19:47, 26 October 2023 (UTC)

Use of $=\infty$ versus $\rightarrow \infty$

The math expression shown under "Infinite strings" section is a divergent series, but currently it is written as $=\infty$. I think this is incorrect because series do not equal infinity. It could be changed to $\rightarrow \infty$ or perhaps just remove the $=\infty$, since its divergence is already stated. Jordanmrfox (talk) 20:48, 1 February 2024 (UTC)

Well, that depends on how you formulate the notion of infinite sum. The statement as written is correct, if you use the appropriate definition. That said, of course in this particular case it doesn't matter much, because a probability can't be greater than 1, so it's already a contradiction once you get that far. --Trovatore (talk) 23:28, 1 February 2024 (UTC)

Thanks for your response. I looked at the wikipedia articles for Series (mathematics), Convergent series, Divergent series, Infinite expression, and I do not see a use of $=\infty$ anywhere.

The page Convergent series uses the arrow notation in expressions like

${1 \over 1}+{1 \over 2}+{1 \over 3}+{1 \over 4}+{1 \over 5}+{1 \over 6}+\cdots \rightarrow \infty .$

If one accepts that the $+\cdots$ means exactly the same thing as summation to infinity, then I think the arrow is the best choice.

However, Borel–Cantelli lemma, which this page cites, uses the $=\infty$ notation a number of times.

Perhaps this is just a stylistic difference between pure math and statistics. I don't think anyone will be seriously confused about what $=\infty$ means, but pedagogically I think we should try to all use the same standard. Jordanmrfox (talk) 21:11, 25 February 2024 (UTC)