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

On 15.12.2024 13:52, Richard Damon wrote:

On 12/15/24 7:00 AM, WM wrote:

On 14.12.2024 23:04, Jim Burns wrote:

If ψ is finite, then ψ+1 is finite.
If ψ+1 is finite, then ψ+2 is finite.

>
Yes, that is the potentially infinite collection of definable numbers. But it explains nothing.

 That is the collection of numbers known as the Natural Numbers, so I guess you are admitting that your "Definable Numbers" include *ALL* of the Natural Numbers

Dark numbers are required to empty ℕ by |ℕ \ {1, 2, 3, ...}| = 0. All definable numbers fail: ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
Regards, WM