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

On 7/17/2024 2:07 PM, WM wrote:

Le 17/07/2024 à 21:48, "Chris M. Thomasson" a écrit :

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!

 Don't claim. Explain how NUF increases.
 

We can say as the unit fractions get smaller and smaller forevermore, that their limit is zero.

 Irrelevant.
 

However, NO unit fraction, no matter how small, ever equals zero. Period.

 Of course not. Therefore NUF cannot change at zero.

If there are no unit fractions then the number of unit fractions is zero. ;^) Anyway, there is no unit fraction that equals zero. Therefore there cannot be a smallest unit fraction. Behold, 0/1 is not a unit fraction! There is no unit fraction that can represent zero. Get over it. However, the largest unit fraction, is good ol' 1/1. :^)