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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Thu, 29 Aug 2024 21:09:33 -0400
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On 8/29/24 9:26 AM, WM wrote:
> Le 28/08/2024 à 22:35, Moebius a écrit :
> 
>> Hint: NUF(x) := card({s e SB : s < x})   (x e IR)
>>
>> Hence NUF(x) = 0 for all x e IR, x <= 0, and NUF(x) = aleph_0 
> 
> 
> for all x > the minimum distance between many unit fractions which is 
> not 0.
> 
> Regards, QM
> 
> 

No, for all x > 0, since there is no finite minimum distance between any 
two unit fractions, as for any attempt to come up with one, there will 
be two unit fractions closer than that.

Note, we aren't talking about "many" unit fractions, but ALL unit fractions.

Your "many" is just a dodge to get around the fact that your logic just 
can't handle them all.