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

On 30.11.2024 12:54, FromTheRafters wrote:

Finite sets versus infinite sets. Finite ordered sets have a last element which can be in the intersection of all previously considered finite sets. Infinite ordered sets have no such last element.

But they have infinitely many elements which contribute to the intersection.
The intersection of the "finite initial segment" of endsegments is
∩{E(1), E(2), ..., E(k)} = E(k)
is a function which remains infinite for all infinite endsegments. If all endsegments remain infinite forever, then this function remains infinite forever.
Regards, WM