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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Wed, 27 Nov 2024 20:15:34 +0100
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On 27.11.2024 18:58, Richard Damon wrote:
> On 11/27/24 12:13 PM, WM wrote:

>> Replacing every element of the set {0, 1, 2, 3, ...} by its successor 
>> yields {1, 2, 3, ..., ω}. The number of ordinals remains the same, the 
>> number of finite ordinals decreases.
> 
> Nope, because omega is NOT the successor for any natural number, the 
> successor of EVERY Natural Number is a Natural Number.

The successor of the last natural number is ω.

> It it the successor for the SET of natural numbers.

And that is nothing else but all natural numbers.

Regards, WM