Re: how

Le 09/04/2024 à 01:22, Richard Damon a écrit :

On 4/8/24 9:44 AM, WM wrote:

Le 07/04/2024 à 19:56, Richard Damon a écrit :

On 4/7/24 9:23 AM, WM wrote:

 

So, With infinite sets, a proper subset CAN be the same size as its parent.

>
Impossible.

>
Nope, PROVEN.

 Proven impossble with my matrix,

 Nope, since you matrix doesn't follow the required form.

It does precilsely.

and we can build such a mapping between the set of natural Numbers (N) with the set of even Numbers (E).

 Only handwaving by "and so on"

In all cases there are infinitely many exceptions.
∀n ∈ ℕ_applied: |ℕ \ {1, 2, 3, ..., n}| = ℵo.

 I didn't say "N_applied", I said N.

But what you can use belongs to ℕ_applied. Otherwise show a natural number that completes the bijection, i.e., which has not infinitely many pairings on front.
Regards, WM