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

Am Wed, 17 Jul 2024 17:17:54 +0000 schrieb WM:

Le 17/07/2024 à 19:01, joes a écrit :

Am Wed, 17 Jul 2024 15:08:30 +0000 schrieb WM:

Le 17/07/2024 à 16:56, Moebius a écrit :

Am 17.07.2024 um 16:43 schrieb WM:

 

Can you explain how NUF(x) can [jump] from 0 [at x = 0] to [aleph_0]
[at any]
point x [> 0] although all unit fractions are separated by finite
distances [...]

Yes, of course: For each and every x e IR, x > 0 there are
countably-infinitely many unit fractions which are <= x. (Hint: No
first one.)

Thema verfehlt. The question is: How does NUF(x) increase from 0 to
more? There is a point where NUF is 0 and then it increases. How?

The same as the sign function.

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

Where do you get this requirement from?
Consider the sign function times infinity.

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Am Fri, 28 Jun 2024 16:52:17 -0500 schrieb olcott:
Objectively I am a genius.