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

Am Thu, 12 Dec 2024 15:23:04 +0100 schrieb WM:

On 12.12.2024 12:30, FromTheRafters wrote:

WM wrote :

 

Most endsegments are infinite.

Many endsegments are infinite too.

Most endsegments are infinite. But if Cantor can apply all natural
numbers as indices for his bijections, then all must leave the sequence
of endsegments. Then the sequence (E(k)) must end up empty. And there
must be a continuous staircase from E(k) to the empty set.

They are all infinite (there are no „dark” numbers).
Every number is a member of only finitely many segments. But the sequence
doesn’t end.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.