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.