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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Replacement of Cardinality
Date: Sat, 17 Aug 2024 12:39:01 -0700
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On 8/17/2024 7:22 AM, Richard Damon wrote:
> 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.

I think so! Wow... ;^o