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

On 06.01.2025 23:43, Jim Burns wrote:

On 1/5/2025 1:14 PM, WM wrote:

>

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.

 ℕ is the set of finite.ordinals.
ℕ holds each finite ordinal.
ℕ holds only finite.ordinals.

>

ℕ| is by definition the smallest transfinite number, larger than every

natural number by every visible factor.

 k ∈ ℕ  ⇒  k+1 ∈ ℕ
is true for both the darkᵂᴹ and the visibleᵂᴹ.

>
One exception exists: ω-1.