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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Fri, 16 Aug 2024 12:07:10 -0400
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On 8/15/24 9:55 AM, WM wrote:
> Le 14/08/2024 à 20:04, Jim Burns a écrit :
>> On 8/14/2024 8:28 AM, WM wrote:
>>> Le 13/08/2024 à 19:42, Jim Burns a écrit :
>>
>>>> The existence of the smallest unit fractions
>>>> is contradictory in the land of
>>>> rationals with
>>>> countable.to numerators and denominators
>>>> with each split situated ==
>>>> a last point in the foresplit or
>>>> a first point in the hindsplit.
>>>
>>> The existence of a smallest unit fraction is
>>> the only alternative to the existence of
>>> more than one at a real point.
>>
>> The NONexistence of a smallest unit fraction is why,
>> for each unit fraction,
>> there are infinitely.many smaller unit fractions.
>> And with no two at one point.
> 
> That is a self-contradiction.
> 
> The first point with unit fractions is x = INVNUF(1).
> 
> Regrads, WM

Which doesn't have a value (at least not in the finite rationals or reals).

That is your problem, NUF isn't properly defined, and thus INVNUF can't 
be properly defined.