Sujet : Re: There is a first/smallest integer (in Mückenland)
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.mathDate : 17. Jul 2024, 19:07:31
Autres entêtes
Organisation : Nemoweb
Message-ID : <51UY0O0Ci9P1zNHagLiR7WfFyVY@jntp>
References : 1 2 3 4 5 6
User-Agent : Nemo/0.999a
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.
>
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.
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
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