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

On 10.01.2025 19:36, joes wrote:

Am Fri, 10 Jan 2025 18:12:15 +0100 schrieb WM:

On 10.01.2025 17:50, joes wrote:

Am Fri, 10 Jan 2025 17:42:39 +0100 schrieb WM:

On 10.01.2025 14:09, joes wrote:

Am Fri, 10 Jan 2025 10:52:46 +0100 schrieb WM:

As I said. You can prove it when doubling all elements of the set

{1, 2,3, ..., ω}.  (*)

You mean N u {w}.

Yes.

 

The regular distance of next neighbours remains as a conserved
property in correct mathematics.

Points don't even exist without the numbers. There is no number with a
finite distance from omega.

Since all natural numbers existing below ω are multiplied by 2, when
doubling the elements of (*), no further numbers below ω can be created
- in actual infinity. What happens with the new 50 % of even numbers?

Why do you want to include omega?

Why not?

What new numbers? There are no evens
above omega.

If actual infinity is invariable, then we can take the set ℕ and consider it as invariable. When we add further elements, it grows. Afterwards it contains further elements. Same can be accomplished by multiplying all natural numbers by 2.
Regards, WM