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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sun, 5 Jan 2025 12:14:47 +0100
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On 04.01.2025 21:38, Chris M. Thomasson wrote:

> For me, there are infinitely many natural numbers, period... Do you 
> totally disagree? 

No. There are actually infinitely many natural numbers. All can be 
removed from ℕ, but only collectively
ℕ \ {1, 2, 3, ...} = { }.
It is impossible to remove the numbers individually
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
Therefore the definable numbers are onl a potentially infinite set.

Regards, WM