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

On 05.01.2025 13:45, Richard Damon wrote:

On 1/5/25 5:40 AM, WM wrote:

For all FISONs:|ℕ \ {1, 2, 3, ..., n}| = ℵo.
That means there is no exception.
>

Just like every natural number is finite,
but the set of *ALL* of them is infinite, each FISON is finite,

>
Not only finite but below 1 % of |ℕ|.

 So? Until you can handle *ALL* of them together, your claim is just a lie about the whole.

As Cantor said actual infinity, for instance omegas and alephs and ℕ are fixed quantities. The set ℕ is invariable. But all finite initial segments of natural numbers FISONs {1, 2, 3, ..., n} cover less than 1 % of ℕ. Proof: {1, 2, 3, ..., 100n} is less than ℕ. That means the set of FISONs will never cover ℕ, nor will its union reach the invariable quantity. The set of FISONs is only potentially infinite, not a fixed quantity but growing over all finite bounds.
Regards, WM