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

On 28.12.2024 16:44, joes wrote:

Am Sat, 28 Dec 2024 15:03:44 +0100 schrieb WM:

ω is the limit of the sequence 1, 2, 3, ... .

It is not a proper limit because the sequence doesn’t converge.

0 is the proper limit of the sequence of unit fractions. That can be translated to ℕ and ω.

 

A separate fact is that ⟦0,ω⦆ ≠ ⟦0,ω⦆∪⦃ω⦄

[0, ω-1] = [0,ω⦆ = ℕ =/= [0, ω]

Undefined. Also you have the infinity of „dark numbers” consecutive
to the naturals.

We have the infinity of dark numbers consecutive to the definable naturals which are a (potentially in-) finite collection.
Regards, WM