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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Sat, 16 Nov 2024 01:27:25 +0100
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Am 15.11.2024 um 22:58 schrieb Chris M. Thomasson:

> Ugg, an infinite set is never exhausted. Taking a gallon of water out of 
> an infinite pool of water means you are holding a gallon water, but the 
> infinite pool is still infinite. The same. Taking an infinite amount of 
> water means the pool is still full of water.

I already told you that this is not necessarily the case.

See: 
https://en.wikipedia.org/wiki/Ross%E2%80%93Littlewood_paradox#Vase_is_empty

Hint: Let's consider your claim: "an infinite set is never exhausted".

But IN \ {1} \ {2} \ {3} \ ... _should_ be {}, I'd say. After all, which 
natural number would "remain" (=be) in the set

               IN \ {1} \ {2} \ {3} \ ...

? :-P

Yeah, slightly "paradoxical". IN \ {1} is infinite, IN \ {1} \ {2} is 
infinite, IN \ {1} \ {2} \ {3} is infinite, etc. Actually, for each and 
everey natural number n: IN \ {1} \ ... \ {n} is infinite (in THIS sense 
your "never" is true). But what's about IN \ {1} \ {2} \ {3} \ ...? 
WHICH natural number would be in this set? :-P

Be aware of the infinite!

Remember:

  > You (WM) are misinterpreting the infinite as
  > ☠( just like the finite, but bigger.

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