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

On 20.01.2025 15:22, FromTheRafters wrote:

WM explained :

On 19.01.2025 13:32, Richard Damon wrote:
>

Note, even in actual infinity, every Natural Number has Aleph_0 successors

>
Then not all could be subtracted from ℕ. But that is possible  ℕ \ {1, 2, 3, ...} = { }.

 All that really says is that the difference set between the set of natural numbers and the set of natural numbers is empty.

It says that all natural numbers without ℵ₀ successors can be handled. This is different for definable natural numbers because there not all natural numbers can be handled:
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
Regards, WM