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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: Fri, 9 Aug 2024 17:29:59 -0700
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On 8/8/2024 4:59 PM, Moebius wrote:
> 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 <.
> 

Yup. Instead if using first, I should say largest... Any better?