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

On 04.01.2025 21:38, Chris M. Thomasson wrote:

For me, there are infinitely many natural numbers, period... Do you totally disagree?

No. There are actually infinitely many natural numbers. All can be removed from ℕ, but only collectively
ℕ \ {1, 2, 3, ...} = { }.
It is impossible to remove the numbers individually
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
Therefore the definable numbers are onl a potentially infinite set.
Regards, WM