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

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} .