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

On 02.12.2024 15:52, joes wrote:

Am Mon, 02 Dec 2024 15:28:30 +0100 schrieb WM:

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

They ARE infinite sets.

 Nevertheless they also contain an infinite set

>

infinitely many elements of which are in the intersection.

The intersection of all infinite segments?

 So it is.

>

An empty intersection cannot
come before an empty endsegment has been produced by losing one element
at every step.

Which happens only in the limit.
>

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).

 

What do you reckon the limit is?
>

Whatever the limit is, it is the same for the sequence of endsegments and the sequence of intersections.