Re: how

Le 04/06/2024 à 23:31, Jim Burns a écrit :

Assumption 2.
ℕ⁺ holds all.and.only numbers countable.to by.1 from.0

Of course. But that is a small minority because you cannot count all:
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
Whatever you count, most numbers remain uncounted.
ℵo is much larger than the collection |ℕ_def| of all counted n.

 We agree if
darkᵂᴹ numbers are countable.to by.1 from.0.

They remain uncounted. Proof:
For all counted n: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
Don't you believe this statement? Or don't you understand it?
Regards, WM