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

On 04.12.2024 16:00, joes wrote:

Am Wed, 04 Dec 2024 14:31:12 +0100 schrieb WM:

In two sets A and B which are non-empty both but have an empty
intersection, there must be at least two elements a and b which are in
one endsegment but not in the other:
a ∈ A but a ∉ B and b ∉ A but b ∈ B.
Same with a set of endsegments. It can be divided into two sets for both
of which the same is required.

Please expand how this works in the infinite case.
 

In every case of empty intersection of non-empty sets at least two such elements must exist. Important is not whether there are few or infinitely many infinite sets but only that the intersection is empty.
Regards, WM