Re: Incompleteness of Cantor's enumeration of the rational numbers

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: hhttps://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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