Re: Replacement of Cardinality

On 8/17/24 9:37 AM, WM wrote:

Le 16/08/2024 à 20:11, joes a écrit :

Am Fri, 16 Aug 2024 16:59:11 +0000 schrieb WM:

 

It does not diminish, there are always infinitely many.

Not according to mathematics: ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 .

I don't see the connection.

 NUF(x) grows from 0 to more, but at no point it grows by more than 1.
 Regards, WM

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.
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. Thus, you argument is you try to "prove" there is a smallest unit fraction, using assumng a function that only exists if there is a smallest unit fraction.
Sorry, your logic, and your brain, has exploded based on contradictions.