Re: Does the number of nines increase?

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

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

the answer to your question is the third option: none.

That is ridiculous.

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?

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.

 

>
Therefore it does not change at 0.

 Functions do not change at single points.

You are wrong. The function f(x) = [x] changes at the points 1, 2, 3, ...

A change needs be _with respect to_ something,

yes, to the value befor that point.

 Consider

No. A person who believes in loss by exchange and NUF changing at 0 is not of interest to me.
Regards, WM