Sujet : Re: Replacement of Cardinality
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.logic sci.mathDate : 14. Aug 2024, 13:32:41
Autres entêtes
Organisation : Nemoweb
Message-ID : <EKWASxeq2sHkaeWKfwPp9--qpzI@jntp>
References : 1 2 3 4 5 6 7 8 9 10
User-Agent : Nemo/0.999a
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
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