Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

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?