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

Le 17/07/2024 à 20:02, Moebius a écrit :

Am 17.07.2024 um 19:49 schrieb WM:

Le 17/07/2024 à 19:13, FromTheRafters a écrit :

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.

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Perhaps, with professional counseling,

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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?

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Sure, it jumps because of your stepwise function.

 Of course it jumps, but what is the maximum size of a jump?

 The jump "at" 0 is THE ONLY jump here,

No, ℵo finite intervals do not fit between [0, 1] and (0, 1].

Hint: img(NUF) = {0, aleph_0}.

It is highly deplorable how acquired "knowledge" can paralyse the brain.
Regards, WM