Re: Replacement of Cardinality

Am 27.08.2024 um 21:22 schrieb Chris M. Thomasson:

On 8/27/2024 12:11 PM, WM wrote:

Le 27/08/2024 à 02:06, Jim Burns 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.

The function exists if actual infinity exists.

That's for sure.

The function does not exist if only potential infinity exists.

Right. card(...) can't be aleph_0 in this case. :-)
Hence we are glad that in the context of axiomatic set theory the AoI ensures for infinite sets. (Cantor ->transfinite set theory).