Sujet : Re: Replacement of Cardinality
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.logic sci.mathDate : 03. Aug 2024, 15:25:03
Autres entêtes
Organisation : Nemoweb
Message-ID : <w2KNEc6WpgYmvVtoH_VZTRkLnUg@jntp>
References : 1 2 3 4 5 6 7 8 9 10
User-Agent : Nemo/0.999a
Le 02/08/2024 à 19:31, Moebius a écrit :
For each and every of these points [here referred to with the variable "x"]: NUF(x) = ℵ₀ .
I recognized lately that you use the wrong definition of NUF.
Here is the correct definition:
There exist NUF(x) unit fractions u, such that for all y >= x: u < y.
Note that the order is ∃ u ∀ y.
NUF(x) = ℵ₀ for all x > 0 is wrong. NUF(x) = 1 for all x > 0 already is wrong since there is no unit fraction smaller than all unit fractions. ℵ₀ unit fractions need ℵ₀*2ℵ₀ points above zero.
Regards, WM