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

On 1/15/25 1:01 PM, WM wrote:

On 14.01.2025 13:37, Richard Damon wrote:
 

And nothing more needs to fit inbetween, as double evey Natural Number is an already existing Natural Number, so none were created.

 That is wrong in actual infinite as well as in potential infinity:
∀n ∈ ℕ: 2n =/= n.
 Regards, WM

So?
No one said that n was 2n. What was said is that the space needed for the natural numbers (that is Aleph_0) is exactly the same as the space needed for the set of two times each natural number (which is also Aleph_0)
That is just one of the provable properties of infinity.