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

On 05.01.2025 19:03, joes wrote:

Am Sun, 05 Jan 2025 12:14:47 +0100 schrieb WM:

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.

Well yes, the size of N is itself not a natural number. Big surprise.
 

ℕ cannot be covered by FISONs, neither by many nor by their union. If ℕ could be covered by FISONs then one would be sufficient. But for all we have: Extension by 100 is insufficient. Every union of FISONs which stay below 1 % stays below 1 %.
1 % is an abbreviation for: Extension by a factor of 100 does not cover ℕ.
Regards, WM
Regards, WM