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May 27

Szekeres Conjecture

Is there something like Szekeres Conjecture, which is different from Erdős–Szekeres theorem? ExclusiveEditor _{Notify Me!} 19:00, 27 May 2024 (UTC)[reply]

The sum will never reach 2

I saw a reference to Zeno's paradoxes#Dichotomy paradox in a comic strip. The article does not mention the sum of 1, one half, one quarter, and so on. Where is that sum?— Vchimpanzee • talk • contributions • 22:34, 27 May 2024 (UTC)[reply]

The sum is 1 if you sum an infinite number of terms. Bubba73 ^{You talkin' to me?} 23:42, 27 May 2024 (UTC)[reply]

Would you believe 2? --142.112.143.8 (talk) 03:59, 28 May 2024 (UTC)[reply]

I was hoping to link the sum I was asking about from the Zeno's paradox article.— Vchimpanzee • talk • contributions • 14:37, 28 May 2024 (UTC)[reply]

Well, Google actually gave me 1/2 + 1/4 + 1/8 + 1/16 + ⋯.— Vchimpanzee • talk • contributions • 14:37, 28 May 2024 (UTC)[reply]

Our article does not mention a sum, but an infinite regression of tasks. Each task has a subtask that must be completed before the whole task can be completed. This is (in Zeno's analysis) as impossible as the task of enumerating all unit fractions in order of magnitude, so that 1/1000 has to come before 1/999 – you can't even start. --Lambiam 15:44, 28 May 2024 (UTC)[reply]

Do you think the Zeno article should mention the other?— Vchimpanzee • talk • contributions • 18:58, 28 May 2024 (UTC)[reply]

To be more precise, the section Dichotomy paradox does not mention this sum. Elsewhere, in the introductory paragraph of the section Paradoxes, it is stated that Zeno's paradoxes are often presented as an issue with the sum of an infinite series, although none of the original ancient sources has Zeno discussing the sum of an infinite series. In my opinion it can be given a place in the analysis of the Achilles and the Tortoise paradox, but not so for Zeno's dichotomy paradox. --Lambiam 20:08, 28 May 2024 (UTC)[reply]