Re: Replacement of Cardinality

Le 13/08/2024 à 19:51, Moebius a écrit :

Am 13.08.2024 um 19:02 schrieb Jim Burns:

On 8/13/2024 10:21 AM, WM wrote:

 

either in a step of size 1
or in a step of size more than 1.

 Let's "assume" that this is true (sort of) for the sake of the argument.
 

But increase by more than 1 is excluded by
the gaps between unit fractions.

 I can't see any argument for this claim.

Deplorable.

 Actually, for each and every real number x > 0 there are infinitely many unit fractions smaller than x:

That is wrong because ℵo unit fractions occupy a nonvanishig real interval, call it y. Then not every point of y has infinitely many unit fractions smaller than it self.

 In fact, Ax > 0: NUF(x) = aleph_0, while NUF(0) = 0.

A very stupid statement. It claims unit fractions smaller than every positive x. "Every positive x" is tantamount to the interval (0, oo).
Regards, WM