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

On 1/20/25 12:15 PM, WM wrote:

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
 

But there are no Natual Numbers without Aleph_0 successors.
So, your "solution" is to a problem that doesn't exist.
Sorry, but all you are doing is showing your logic is built on lies and inconsistencies.