Re: Contradiction of bijections as a measure for infinite sets

Le 09/04/2024 à 20:27, Jim Burns a écrit :

On 4/9/2024 8:22 AM, WM wrote:

Le 09/04/2024 à 01:54, Jim Burns a écrit :

On 4/8/2024 9:55 AM, WM wrote:

Le 07/04/2024 à 21:47, Jim Burns a écrit :

 

The successor operation is closed in
the natural numbers.

>
For visible numbers only.

>
Visibleᵂᴹ or darkᵂᴹ,
k is a natural number  :⟺
k=0 ∨ ∃⟦0,k⦆: ∀i ∈ ⟦0,k⦆: i⁺¹ ∈ ⦅0,k⟧

>
Not correct if
there are all natural numbers such that
no further one exists below ω.

 You seem to be saying:
| Not correct if
| not all natural numbers have
| a further one below ω

All further numbers are multiplied too.

 In other words [1]:
| Not correct if
| ω is finiteⁿᵒᵗᐧᵂᴹ.

Not correct if there is no free space between ℕ and ω.
Regards, WM