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

Am Mon, 02 Dec 2024 15:28:30 +0100 schrieb WM:

On 02.12.2024 12:53, FromTheRafters wrote:
 

Endsegment E(n) = {n, n+1, n+2, ...}

This is his definition of endsegment, which as almost anyone can see,
has no last element, so yes it is infinite. He says 'infinite
endsegment' as if there were a choice, only to add confusion.

Infinite endsegments contain an infinite set each

They ARE infinite sets.

infinitely many elements of which are in the intersection.

The intersection of all infinite segments?

An empty intersection cannot
come before an empty endsegment has been produced by losing one element
at every step.

Which happens only in the limit.

E(1), E(2), E(3), ...
and E(1), E(1)∩E(2), E(1)∩E(2)∩E(3), ...
are identical for every n and in the limit because E(1)∩E(2)∩...∩E(n) =
E(n).

What do you reckon the limit is?

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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.