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

On 28.11.2024 20:45, joes wrote:

Am Thu, 28 Nov 2024 18:46:21 +0100 schrieb WM:

The intersection of all infinitely many segments is empty.

Of course, when all ℵo numbers have become indices, then there is no number left as contents. Before, until any E(n), there are not infinitely many endsegments.

The infinite intersection is empty.

Of course. Then no natnumber is in all endsegments. All contents has gone. Otherwise there are not infinitely many indices indexing as many endsegments.

 

Every infinite endsegments has an infinite intersection with all its
predecessors.

Itself, yes.

If there are only infinite endsegments, then all have an infinite intersections with all their predecessors. Other infinite endsegments do
Regards, WM