Re: Replacement of Cardinality

On 8/4/2024 8:35 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?
Impossible. ℵ₀ unit fractions occupy ℵ₀*2^ℵ₀ points. Not even one unit fraction cann be smaller than all positive x.

Huh? Say x = 1/2, there are infinite smaller unit fractions, say, 1/4, 1/5, 1/6, ect... However there is only one larger one, 1/1. See? No smallest one for 1/0 is not a unit fraction! There is a largest one, 1/1...
They tend to zero, but there is no smallest one...
See?