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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality (infinite middle)
Date: Fri, 09 Aug 2024 06:25:20 -0400
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Ross Finlayson explained :
> On 08/08/2024 03:30 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.
>
> Of course, you can start with a first and last element,
> then make infinitely-many in the middle.
>
> 0 ... ( ... infinitely-many ... ) ... infinity

Sometimes you are as bad as he is. :)