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

On 9/6/24 8:22 AM, WM wrote:

On 06.09.2024 00:36, Python wrote:

Le 05/09/2024 à 22:44, crank Wolfgang Mückenheim, aka WM a écrit :

 

>
You are mistaken. I do not conclude the latter from the former. I conclude the latter from the fact that NUF(0) = 0 and NUF(x>0) > 0 and never, at no x, NUF can increase by more than 1.

>
What the Hell could mean "to increase at an x" ?

 Example: The function f(x) = [x] increases at every x ∈ ℕ by 1.
The function NUF(x) increases at every x = unit fraction 1/n by 1.
It does not increase at 0 because 0 is not a unit fraction.
 Regards, WM

Except that is can't because there is no "smallest" unit fraction to count from.
Thus, either NUF(x) increases at some sub-finite values, or it doesn't exists.
Sorry, you just don't understand that you need to show existance and not just presume it.