Re: How many different unit fractions are lessorequal than all unit fractions?

On 9/6/24 8:07 AM, WM wrote:

On 06.09.2024 05:08, Richard Damon wrote:

On 9/5/24 10:08 AM, WM wrote:

 

NUF(x) must grow. It cannot grow by more than 1 at any x.

 

This is NOT the "ancient" idea of infinity,

 NUF(x) must grow. It cannot grow by more than 1 at any x.
Right or wrong in your opinion?
 Regards, WM
 

Only if it exists.
If it does, it must be counting some sub-finite values as "unit fractions" that are not the reciprocal of the Natural Numbers (since there is no smallest of those unit fractions to count from).
So, either it is counting some sub-finite values (actually a lot of them a countable infinity of them) or it just doesn't exist.
Maybe that is your dark numbers, these sub-finite numbers that are reciprocals of some post-finite values above the infinite set of Natural Numbers (which have no upper bound) and are below Omega.