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

Am Thu, 12 Dec 2024 15:25:59 +0100 schrieb WM:

On 12.12.2024 13:26, Richard Damon wrote:

On 12/12/24 4:12 AM, WM wrote:

 

Note, "inifinite" isn't a Natural Number,

But a state,often dscribed byan infinite whole number.
 

or a Real Number, so NO segement, specified by values, can have an
"infinte endsegment".

Every infinite segment is an infinite segment

Yes, well.

and therefore has an infinite segment as subset.

Getting close here…

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.

Yes, in the limit. There is no natural k such that E(k) is empty.

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

This is where you are mistaken. How do you get from naturals to
finite dark numbers anyway?

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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.