Sujet : Re: There is a first/smallest integer (in Mückenland)
De : invalid (at) *nospam* example.invalid (Moebius)
Groupes : sci.mathDate : 17. Jul 2024, 19:02:08
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v790v0$1ue32$3@dont-email.me>
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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, Mückenheim: For x <= 0 NUF(x) = 0 and for ALL x > 0 NUF(x) = aleph_0. So the answer is: aleph_0.
Hint: img(NUF) = {0, aleph_0}.
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