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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
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 12:50:24 -0700
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On 7/17/2024 10:01 AM, joes wrote:
> 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. There simply is no such "point", as
> there is no least positive number. The distances between unit
> fractions get infinitely small.
> 

Right!