Re: Replacement of Cardinality

Le 04/08/2024 à 17:53, Jim Burns a écrit :

On 8/4/2024 11:35 AM, WM wrote:

Le 04/08/2024 à 02:15, Moebius a écrit :

Am 03.08.2024 um 21:54 schrieb Jim Burns:

On 8/3/2024 10:23 AM, WM wrote:

 

NUF(x) = ℵ₀ for all x > 0 is wrong.

>
Nonsense.
>
Actually, Ax > 0: NUF(x) = ℵ₀.

>
You mean that there are
ℵ₀ unit fractions smaller than all positive x?

 No, he doesn't mean that.

NUF(x) = ℵ₀ means exactly that.

You (WM) have mad an unreliable quantifier shift.

I have defined my function this way.

ℵ₀ unit fractions occupy ℵ₀*2^ℵ₀ points.
Not even one unit fraction can be
smaller than all positive x.

Can you (JB) understand that?
If so, can you define a function expressing just that?
Or do you feel it a sacrilege to explicitly express that?
Regards, WM
Regards, WM