Re: Replacement of Cardinality

On 8/21/24 6:43 AM, WM wrote:

Le 20/08/2024 à 22:05, Jim Burns a écrit :

On 8/20/2024 9:07 AM, WM wrote:

 

No min.⅟ℕᵈᵉᶠ exists.

 The reason is potential infinity. But dark unit fractions are assumed to be actually infinite.

>

It starts from 0.

>
If ⅟ℕᵈᵉᶠ starts,
⅟ℕᵈᵉᶠ starts from min.⅟ℕᵈᵉᶠ
>
No min.⅟ℕᵈᵉᶠ exists.
⅟ℕᵈᵉᶠ does not start.
>
Because 0 is glb.⅟ℕᵈᵉᶠ not.in ⅟ℕᵈᵉᶠ

 All that is correct for definable unit fractions.
But NUF(x) starts from 0 and cannot avoid to take the values 1, 2, 3, ... .
 Regards, WM
 

And thus must be doing so at things that are not the reciprical of Natural Numbers, since there is no such thing as the first unit fraction of Natural numbers, since there is no highest Natural Number.
Thus your NUF must be counting trans-finite unit fractions, which you call dark so you don't see that they are not real unit fractions.
Maybe the first dark unit fraction is at 1/Omega or 1/(Omega-1)