Re: Replacement of Cardinality

Am Fri, 30 Aug 2024 12:59:47 +0000 schrieb WM:

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.

What do you mean by „reducing”? That the number of unit fractions
stays infinite when cutting off the right?

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

Are there two unit fractions possible lessorequal than all unit
fractions?

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.