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

Am 11.01.2025 um 05:21 schrieb Moebius:

Am 11.01.2025 um 04:51 schrieb Moebius:

Am 10.01.2025 um 23:18 schrieb Chris M. Thomasson:

On 1/10/2025 1:52 AM, WM wrote:

 

Then for every [ordinal number] it is determined whether [it] is a natural number [or not].

>
Indeed!

 There is even a simple criteria for this (i.e. if an ordinal number is a natural number or not):
            For each and every ordinal number x:
            x is a natural number iff x < omega.

Hence of course:
             For each and every ordinal number x:
             x is NOT a natural number iff x >= omega.

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