Re: Replacement of Cardinality

Am Sat, 03 Aug 2024 14:25:03 +0000 schrieb WM:

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.

It is the definition you have previously used.

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.

You are specifying an exact number, not only at least one.

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.

New sig.

ℵ₀ unit fractions need ℵ₀*2ℵ₀ points above zero.

--
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.