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

On 07.09.2024 04:01, Richard Damon wrote:
 > On 9/6/24 8:07 AM, WM wrote:
 >> NUF(x) must grow. It cannot grow by more than 1 at any x.
 >> Right or wrong in your opinion?
 > Only if it exists.
There is no reason to deny its existence. If there is zero and all real numbers x > 0 and if there are unit fractions, then we can ask how many unit fractions are between 0 and any x.
 >
 > If it does, it must be counting some sub-finite values as "unit fractions" that are not the reciprocal of the Natural Numbers
Only reciprocals of natural numbers are counted.
 > (since there is no smallest of those unit fractions to count from).
Perhaps you consider only definable natural numbers. They have no largest element.
 > 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.
Dark numbers are post finitely definable.
Regards, WM