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

On 08.01.2025 00:50, Jim Burns wrote:

On 1/7/2025 4:13 AM, WM wrote:

The cardinal:ordinal distinction
-- which does not matter in the finite domain
matters in the infinite domain.

The reason is that the infinite cardinal ℵ₀ is based on the mapping of the potentially infinite collection of natural numbers n, all of which have infinitely many successors. The cardinal ℵ₀ is not based on the mapping of the actually infinite set ℕ where ℕ \ {1, 2, 3, ...} = { }.
Regards, WM