Sujet : Re: Replacement of Cardinality
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 19. Aug 2024, 12:29:50
Autres entêtes
Organisation : Nemoweb
Message-ID : <ytwMFNd1tHmxk476VR9KrOdeYfw@jntp>
References : 1 2 3 4 5 6 7 8 9 10
User-Agent : Nemo/0.999a
Le 17/08/2024 à 16:22, Richard Damon a écrit :
On 8/17/24 9:37 AM, WM wrote:
NUF(x) grows from 0 to more, but at no point it grows by more than 1.
And there is "no point" that is smaller than all unit fractions but greater than 0, so at that point NUF(x) jumps from 0 to Aleph_0.
That is superstition.
Your problem is NUF(x) may have a clear verbal description, but not a mathematical one, as it is based on a false assumption that there exists a smallest unit fraction.
That is not an assumption but it is derived from the mathematics:
∀n ∈ ℕ: 1/n - 1/(n+1) > 0 Regards, WM
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