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

WM was thinking very hard :

On 12.12.2024 12:30, FromTheRafters wrote:

WM wrote :

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Most endsegments are infinite.

 Many endsegments are infinite too.

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Most endsegments are infinite.

Some 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.

Impossible, since k and k+1 etcetera are natural numbers.

And there must be a continuous staircase from E(k) to the empty set.

A limit set or element does not have to be completely within a set or interval.