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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: Thu, 9 Jan 2025 14:06:11 +0100
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On 09.01.2025 13:27, FromTheRafters wrote:
> WM wrote :
>> On 09.01.2025 01:07, joes wrote:
>>> Am Wed, 08 Jan 2025 22:57:52 +0100 schrieb WM:
>>
>>>> The rule is for n there is n+1. But the successor is not created but
>>>> does exist. How far do successors reach? Why do they not reach to ω-1?
>>>> Where do they cease before?
>>> They don't cease. They simply aren't in the same league, if you will.
>>
>> Cantor will. Every set of numbers of the first and second number class 
>> has a smallest element. Hence they all are on the ordinal line.
> 
> Zero is the smallest in the natural number class, omega is the smallest 
> of the infinite number class. Neither has a predecessor in its class.

Are the natural numbers fixed or do they evolve?

Regards, WM