Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how

On 5/8/2024 3:55 PM, WM wrote:

Le 07/05/2024 à 00:11, Jim Burns a écrit :

All which canNOT be counted.to are not.in ℕ

>
All which canNOT be counted.to are not.in ℕ_def.

And all which CAN be counted.to are in ℕ_def.
ℕ_def is the set of all and only
numbers which CAN be counted.to.
ℕ_def is what everyone else calls ℕ
|ℕ_def| = ℵ₀
∀n ∈ ℕ_def:
|{m ∈ ℕ_def: m > n}| = ℵ₀
¬∃k ∈ ℕ_def:
An ∈ ℕ_def:
k ∈ {m ∈ ℕ_def: m > n}
ℕ_def is infinite.
"Infinite" doesn't mean "humongous".

∀n ∈ ℕ_def: ∃^ℵo m ∈ ℕ, m > n.

∀n ∈ ℕ_def: ∃^ℵo m ∈ ℕ_def, m > n.

∀n ∈ ℕ: ~∃^ℵo n ∈ (ℝ\ℕ).

You probably want to say that,
☠ in ℕ
☠ there are numbers with fewer than ℵ₀.many after.
☠ ∃n ∈ ℕ:
☠ |{m ∈ ℕ: m > n}| < ℵ₀
(There aren't.)
ℕ which you describe that way
is not
ℕ which everyone calls ℕ
"Infinite" doesn't mean "humongous".