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

On 06.12.2024 17:31, joes wrote:

Am Fri, 06 Dec 2024 14:10:10 +0100 schrieb WM:

On 06.12.2024 13:23, joes wrote:

Am Thu, 05 Dec 2024 22:31:01 +0100 schrieb WM:

>

If all natnumbers have been lost, then nothing remains. If there are
infinitely many endsegments, then all contents has become indices.

This happens only in the limit. And then there are no more numbers.

It happens in the end. ∀k ∈ ℕ : E(k+1) = E(k) \ {k}.

"The end" is not a natural number.

It is not a visible natural number.

 

Two identical sequences have the same limit. E(1)∩E(2)∩...∩E(n) =
E(n).
As long as all endsegments are infinite so is their intersection.

Only as long as you only consider a finite number of them.

As long as all endsegments are infinite, there is no infinite number of
them.

It's your fault of not considering all infinitely many segments at once.

"At once" is the seductive attempt of tricksters. All that happens in a sequence can be investigated at every desired step.
Regards, WM