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

On 10/31/24 11:38 AM, WM wrote:

On 31.10.2024 12:00, FromTheRafters wrote:
 

Failure to recognize that discontinuity is mathematical noted.

 False. NUF(x) can only increase at unit fractions. They cause no larger discontinuity than 1.
 Regards, WM
 

It only increase at unit fractions if it is defined to be the number of unit fractions less than or equal to its parameter.
If it is just less than, then it increase AFTER the unit fraction, and the is no specific point there to increase at.
If it IS defined as the number of unit fractions less than or equal to its parameter, then it would only have the value of 1 at the first unit fraction, which doesn't exist.
Since the thing it is defined to change at has an accumulation point, it can have a discontinuity, even if it only changes by "1" at those points (because it hits the problem of there not being a first point to increment at).