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

On 09.12.2024 20:18, Python wrote:

Le 08/12/2024 à 23:34, Crank Wolfgang Mückenheim from Hochschule Augsburg aka WM a écrit :

On 08.12.2024 19:01, Jim Burns wrote:

On 12/8/2024 5:50 AM, WM wrote:

>

∀n ∈ ℕ: E(1)∩E(2)∩...∩E(n) = E(n)
What can't you understand here?

>
{E(i):i} is the set.of.all non.empty end.segments.
>
⋂{E(i):i} is the intersection.of.all

non.empty end.segments.

>
∀n ∈ ℕ:
{E(i):i}∪{E(n+1)} = {E(i):i}
Each is "already" in.

>
Not the empty endsegment.
∀n ∈ ℕ: E(n) is non-empty. But not every E(n+1).

 You could hardly write something worse and more wrong that that.
 The very core property of N is that if n ∈ ℕ then n+1 ∈ ℕ.

That is correct for definable natural numbers and even for almost all dark natural numbers.
The very core property of analysis is that equal sequences have equal limits if they have limits at all.
Regards, WM