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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: =?UTF-8?Q?Re=3A_There_is_a_first/smallest_integer_=28in_M=C3=BCcken?=
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Date: Wed, 17 Jul 2024 16:56:08 +0200
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Am 17.07.2024 um 16:43 schrieb WM:
> Le 17/07/2024 à 13:37, Moebius a écrit :

>> 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.
> 
> 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.)

Not that hard, is it?

Relevance concerning your nonsensical claim "This is true but difficult 
to understand"? - None.