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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: Replacement of Cardinality
Date: Sat, 17 Aug 2024 10:22:03 -0400
Organization: i2pn2 (i2pn.org)
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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.