Sujet : Re: There is a first/smallest integer (in Mückenland)
De : invalid (at) *nospam* example.invalid (Moebius)
Groupes : sci.mathDate : 18. Jul 2024, 07:00:07
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v7ab17$29gck$1@dont-email.me>
References : 1 2 3 4 5 6 7
User-Agent : Mozilla Thunderbird
Am 18.07.2024 um 07:52 schrieb Moebius:
Am 18.07.2024 um 06:30 schrieb Jim Burns:
On 7/17/2024 1:49 PM, WM wrote:
Le 17/07/2024 à 19:13, FromTheRafters a écrit :
>
Sure, it jumps because of your stepwise function.
>
Of course it jumps, but what is the maximum size of a jump?
>
|ℝ| is the maximum size of a jump.
Nope. |IN| (aleph_0) is "the maximum size of a jump", namely "the size" of the jump "at" 0. (Hint: NUF has only one jump, namely "at" 0.)
Hint: NUF(x) := |{u e {1/n : n e IN} : u <= x}| (x e IR) .
Hence
NUF(x) = 0 for all x e IR, x <= 0
and
NUF(x) = aleph_0 for all x e IR, x > 0 ,
as well as
img(NUF) = {0, aleph_0} .
…