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From: Moebius <invalid@example.invalid>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Fri, 9 Aug 2024 01:59:35 +0200
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Am 08.08.2024 um 22:36 schrieb Chris M. Thomasson:
> 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 [i.e. smallest] element.
> 
> The first unit fraction is 1/1, there is no last one...

Nope. We are using the usual order < defined on IR to determine if there 
is a first (smallest) / last (largest) unit fraction.

So there is no first/smallest unit fraction and there is a last/largest 
unit farction (namely 1/1), in respect to <.