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

On 14.12.2024 12:00, joes wrote:

Am Sun, 08 Dec 2024 11:55:34 +0100 schrieb WM:

On 08.12.2024 11:43, joes wrote:

Am Sat, 07 Dec 2024 22:50:27 +0100 schrieb WM:

>

∀n ∈ ℕ: E(1)∩E(2)∩...∩E(n) = E(n)
All n are infinitely many.

That sentence only talks about a single n at a time, though,
not about the infinite intersection.

It talks about all n and therefore about all E(n).

No, it says nothing about the intersection of all E(n),
only about finite intersections

All E(n) have finite indices n. But the quantifier-nonsense is no longer under discussion because the intersections are sufficient and accepted as becoming empty. And their procedure is the same as that of the endsegments:
∀k ∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k}).
Regards, WM