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From: Moebius <invalid@example.invalid>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Sat, 10 Aug 2024 00:36:20 +0200
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Am 09.08.2024 um 05:34 schrieb Jim Burns:
> On 8/8/2024 5:56 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 [...]  element.
>>>
>>> The first unit fraction is 1/1, there is no last one...
>>
>> ... or there is a last one but no first one.

Which is the case in respect to the usual < defined on ÌR.

1/1 is the <-largest/last unit fraction and there is no <-smallst/first 
unit fraction. Rather simple facts. Expect in Mückenhausen of course,