Re: Does the number of nines increase?

Le 08/07/2024 à 22:44, joes a écrit :

Am Mon, 08 Jul 2024 19:57:33 +0000 schrieb WM:

Le 08/07/2024 à 19:33, Jim Burns a écrit :

On 7/8/2024 9:49 AM, WM wrote:

 

There is no point x > 0: NUF(x) < ℵ₀

That is wrong because 10 unit fractions and their finite distances
occupy a part of the positive axis which has a finite positive measure.
Therefore there exist x > 0: NUF(x) < 11. in order to accumulate ℵ₀ unit
fractions, at least 10 must exist at the beginning. Are you unable to
understand that?

Which ten.

There cannot be ℵ₀ without first 10.

 

There is no point x < 0: NUF(x) > 0 NUF(x) changes "at" 0.

The function f(x) = [x] changes at 1 from 0 to 1, at 2 from 1 to 2, and
so on.
The function NUF(x) changes at unit fractions by 1, but not before, not
at 0.

NUF changes at 0 from 0 to omega.

Are all mathematicians so stupid?
Regards, WM