Re: Replacement of Cardinality

Le 31/07/2024 à 19:33, Jim Burns a écrit :

On 7/31/2024 9:59 AM, WM wrote:

Le 30/07/2024 à 20:37, Jim Burns a écrit :

 

NUF(x) = |⅟ℕ∩(0,x]| = ℵ₀
does not imply any unit fraction outside (0,x]

>
But it implies that you can use only
x having ℵ₀ smaller positive points,
in fact even ℵ₀*2ℵ₀.
>
∀ x > 0: NUF(x) = ℵ₀ would be wrong.

 Each non.{}.subset of ⅟ℕ∩(0,1] is maximummed.
  ∀S ⊆ ⅟ℕ∩(0,1]: S ≠ {}  ⇒  ∃u = max.S

In the dark domain the maximum cannot be discerned.

 Each unit.fraction in ⅟ℕ∩(0,1] is down.stepped.
  ∀u ∈ ⅟ℕ∩(0,1] ∃v = ⅟(1+⅟u) = max.⅟ℕ∩(0,u)

Assuming all this would lead to potential infinity.
I assume actual infinity however. There are dark numbers. There is a greates natnumber. There is no chance to lose Bob.
Regards, WM