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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: Wed, 8 Jan 2025 10:16:00 +0100
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On 08.01.2025 00:50, Jim Burns wrote:
> On 1/7/2025 4:13 AM, WM wrote:

> The cardinal:ordinal distinction
> -- which does not matter in the finite domain
> matters in the infinite domain.

The reason is that the infinite cardinal ℵ₀ is based on the mapping of 
the potentially infinite collection of natural numbers n, all of which 
have infinitely many successors. The cardinal ℵ₀ is not based on the 
mapping of the actually infinite set ℕ where ℕ \ {1, 2, 3, ...} = { }.

Regards, WM