Re: There is a first/smallest integer (in Mückenland)

On 7/17/2024 10:13 AM, FromTheRafters wrote:

WM presented the following explanation :

Le 17/07/2024 à 15:42, FromTheRafters a écrit :

Moebius presented the following explanation :

WM> All unit fractions are separated. Therefore there is a first one
>
Moebius> All integers are separated. Therefore there is a first one [?]
>
WM> This is true but difficult to understand.

>
Perhaps, with professional counseling,

>
you could explain how NUF(x) can increase from 0 to many more in one point although all unit fractions are separated by finite distances?

 Sure, it jumps because of your stepwise function.

Real line going to the right:
(0)->(1/1)
There is no so-called smallest unit fraction that magically sits next to zero! Damn it WM! We can say as the unit fractions get smaller and smaller forevermore, that their limit is zero. However, NO unit fraction, no matter how small, ever equals zero. Period.