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

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:

>

Hint: The set of all natural numbers, IN, does not change.

So all natural numbers are fixed. Then for every point on the ordinal
line it is determined whether there is a natural number. Although we
cannot determine it because most are dark.

There are no points without numbers.

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

{1, 2,3, ..., ω}.  (*)

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?
Regards, WM