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

On 11.01.2025 14:34, joes wrote:

1, 2, 3, 4, 5, ..., ω becomes 2, 4, 6, 8, 10, ..., ω, ω+2, ω+4, ..., ω2.

No. There is no x e N such that 2*x >= omega. You have listed two
consecutive infinities on the right.

There is a basic law: When a sequence of regular distances is multiplied by 2, then a sequence of regular distances results.
The interval (0, ω)*2 becomes (0, ω*2) with ω in the middle. Below ω the newly created even numbers cannot be inserted, because more than all even natural numbers do not exist in actual infinity.
Every contrary opinion is based on potential infinity.
Regards, WM