Sujet : Re: Replacement of Cardinality
De : chris.m.thomasson.1 (at) *nospam* gmail.com (Chris M. Thomasson)
Groupes : sci.logic sci.mathDate : 05. Aug 2024, 00:07:37
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v8p1jp$9gvr$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
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?
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