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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Thu, 09 Jan 2025 07:27:31 -0500
Organization: Peripheral Visions
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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.