Re: Replacement of Cardinality

On 8/30/24 8:59 AM, WM wrote:

Le 30/08/2024 à 12:13, Moebius a écrit :

Am 30.08.2024 um 09:21 schrieb joes:

 

Thus: The interval (0, x) contains finitely many unit fractions only
for infinitesimal x.

>
Actually, it either contains NO unit fractions (if x = 0 or x is infinitesimal but > 0) or it contains infinitely many (ℵo) unit fractions.

 That contradicts the fact that ℵo unit fractions occupy an interval that can be reduced.

>
So no matter if x > 0 is infinitesimal or not: NUF(x) =/= 1.

 Are there two unit fractions possible lessorequal than all unit fractions?
 Regards, WM
 

No, because nothing is smaller than itself, and two unequal order things must have an order.
But there ARE two unit fractions less than ANY given unit fraction.
You just apply the wrong qualifiers because you logic system is broken.