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

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, infinitely many elements of which are in the intersection. An empty intersection cannot come before an empty endsegment has been produced by losing one element at every step.
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).
Regards, WM