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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Does the number of nines increase?
Date: Tue, 9 Jul 2024 23:17:51 +0200
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Am 09.07.2024 um 22:42 schrieb Chris M. Thomasson:
> On 7/9/2024 9:53 AM, WM wrote:
>> Le 09/07/2024 à 16:35, Moebius a écrit :
>>> Am 09.07.2024 um 15:23 schrieb joes:
>>>> Am Tue, 09 Jul 2024 11:49:21 +0000 schrieb WM:
>>>
>>>>> many don't understand that ℵo unit fractions cannot occupy a distance
>>>>> smaller than all positive distances. Can you?
>>>
>>>> What does this mean? It should read "smaller than ANY".
>>>
>>> Es bedeutet, dass Mückenheim (in diesem Kontext) nicht zwischen AxEy 
>>> und EyAx unterscheiden kann.
>>
>> That is nonsense. Either there is a first unit fraction or this is not 
>> the case. 
> 
> There is a first unit fraction at 1/1. However, there is no last unit 
> fraction... :^)

No, with "first" he means a "smallest" unit fraction. Hence from this 
point of view 1/1 is the "last" (i.e. largest) unit fraction.

      ... < 1/3 < 1/2 < 1/1.

WM's claim is that there is a unit fraction WM such that

      Au e {1/n : n e IN}: WM <= u

In other words:

      WM < ... < 1/3 < 1/2 < 1/1 ,

such that there is no unit fraction u with

      u < WM < ... < 1/3 < 1/2 < 1/1 .

Of course, this doesn't MAKE any sense (i.e. is bullshit). After all, 
1/(1/WM + 1) would be a unit fraction with

      1/(1/WM + 1) < WM < ... < 1/3 < 1/2 < 1/1 .