Re: Does the number of nines increase?

On 7/9/2024 2:17 PM, Moebius wrote:

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".

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Es bedeutet, dass Mückenheim (in diesem Kontext) nicht zwischen AxEy und EyAx unterscheiden kann.

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That is nonsense. Either there is a first unit fraction or this is not the case.

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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.

That is backwards!?!?!?! Shit. There is a largest unit fraction at 1/1, every other one is smaller, forever and ever...

       ... < 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 .
 

Shit.