Re: Replacement of Cardinality

On 8/27/24 3:57 PM, WM wrote:

Le 27/08/2024 à 21:31, Moebius a écrit :

On 8/25/2024 3:45 PM, WM wrote:

>

This function exists because
nothing contradicts its existence.

>
Right. But the values of the function NUF are:
>
0 for all real arguments <= 0 and aleph_0 for all real arguments > 0.

 Correction: For all ends of real intervals containing ℵo unit fractions. The interval (0, x) cannot contain ℵo unit fractions unless x is sufficiently large.
 Regards, WM

But sufficiently large is just being any finite positive number.
Then it contains the Aleph_0 unit fractions starting at 1/ceil(1/x)
Since it is a fact that for ANY Natural Number n, there are aleph_0 other Natural Numbers after it, since aleph_0 is not exhausted by trying to reduce it by finite amounts.