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

On 01.12.2024 12:59, joes wrote:

Am Sat, 30 Nov 2024 20:10:49 +0100 schrieb WM:

There is an infinite sequence of endsegments E(1), E(2), E(3), ... and
an infinite sequence of their intersections E(1), E(1)∩E(2),
E(1)∩E(2)∩E(3), ... .
Both are identical - from the first endsegment on until every existing
endsegment.

How surprising.

For most set theorists certainly.

Of course. Only for finite k the endsegments are infinite.

All natural k are finite.

Then all endsegments are infinite like their intersections.

...for every natural (which are finite), but not for the limit.

The limit cannot differ from all endsegments E(k) by more than one elements because infinitely many natnumbers cannot disappear in between.
∀k ∈ ℕ : E(k+1) = E(k) \ {k}. Who should eat up the infinitely many natnumbers?
Regards, WM