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

On 08.12.2024 11:46, joes wrote:

Am Sat, 07 Dec 2024 22:37:04 +0100 schrieb WM:

 

∀n ∈ ℕ: E(1)∩E(2)∩...∩E(n) = E(n).
Every counter argument has to violate this. That is inacceptable.

Incorrect. "More than finite" means infinite. Your formula only talks
about finite intersections.

It talks about all finite intersections.

Each finite.cardinality cannot be more.than.finitely.many

So it is. Each finite cardinal cannot turn a finite set into an
infinite set. But even for infinite sets we have ∀n ∈ ℕ:
E(1)∩E(2)∩...∩E(n) = E(n).

That is not an infinite intersection.

It is the sequence of all endsegments and of all finite intersections.
The limits of identical sequences are identical

∀n ∈ ℕ: E(1)∩E(2)∩...∩E(n) = E(n).
No empty intersection without an empty endsegment.

That happens, as you know, only in the limit.

And what is the limit?