Path: ...!weretis.net!feeder8.news.weretis.net!pasdenom.info!from-devjntp
Message-ID: <Eb-CQaKSaHkMpWykEcQGtifvbV0@jntp>
JNTP-Route: news2.nemoweb.net
JNTP-DataType: Article
Subject: Re: There is a first/smallest integer (in =?UTF-8?Q?M=C3=BCckenland=29?=
References: <v78aei$1qhrg$2@dont-email.me> <iez0JhnP5QUwPTJ47oubeE1Aq5M@jntp> <v78m28$1sk3g$1@dont-email.me>
 <7mXj2D8kEhAscu3HLTqTUKsaj18@jntp> <d9b0dacd61b979099d931df69cf76c214d690d39@i2pn2.org>
Newsgroups: sci.math
JNTP-HashClient: IwN5iwyprmSrB_c_k_JDEKr0_X4
JNTP-ThreadID: v78aei$1qhrg$2@dont-email.me
JNTP-Uri: http://news2.nemoweb.net/?DataID=Eb-CQaKSaHkMpWykEcQGtifvbV0@jntp
User-Agent: Nemo/0.999a
JNTP-OriginServer: news2.nemoweb.net
Date: Wed, 17 Jul 24 17:17:54 +0000
Organization: Nemoweb
JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/126.0.0.0 Safari/537.36
Injection-Info: news2.nemoweb.net; posting-host="82b75c1d0a83e677ff646b52485f72f8b23749df"; logging-data="2024-07-17T17:17:54Z/8952670"; posting-account="217@news2.nemoweb.net"; mail-complaints-to="julien.arlandis@gmail.com"
JNTP-ProtocolVersion: 0.21.1
JNTP-Server: PhpNemoServer/0.94.5
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
X-JNTP-JsonNewsGateway: 0.96
From: WM <wolfgang.mueckenheim@tha.de>
Bytes: 2412
Lines: 29

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.

> There simply is no such "point", as
> there is no least positive number. The distances between unit
> fractions get infinitely small.

They remain finite in every case.

Regards, WM