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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Thu, 8 Aug 2024 15:14:43 -0700
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On 8/8/2024 2:56 PM, FromTheRafters wrote:
> Chris M. Thomasson has brought this to us :
>> On 8/8/2024 3:30 AM, FromTheRafters wrote:
>>> on 8/8/2024, WM supposed :
>>>> Le 08/08/2024 à 00:17, Moebius a écrit :
>>>>
>>>>> Actually, his "thinking process" is simple:
>>>>>
>>>>> "Since there is a gap (space) between adjacent unit fractions and 
>>>>> all unit fractions are in the interval (0, 1], there must be 
>>>>> FINITELY MANY of them (i.e. a first/smallest one)."
>>>>
>>>> No, that is nonsense. There are not finitely many unit fractions.
>>>
>>> Then stop assuming that there is a first and last element.
>>
>> The first unit fraction is 1/1, there is no last one...
> 
> ... or there is a last one but no first one.

:^) Depends on your path... ;^) Going from 1 to 0, or 0 to 1.

So:

(0/1)->...->(1/1)

(0/1) is not a unit fraction so there is no first one in this context.

However, going from:

(1/1)->...->(1/0)

There is a first one in this context.

I generally consider (1/1) to be the first unit fraction.

The main point is that there is no smallest unit fraction and there is 
no largest natural number... :^)