Re: Does the number of nines increase?

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 .