Path: ...!news.nobody.at!weretis.net!feeder8.news.weretis.net!pasdenom.info!from-devjntp
Message-ID: <vol0FSJMuqv_Uox5qeHDiF8wsA4@jntp>
JNTP-Route: news2.nemoweb.net
JNTP-DataType: Article
Subject: Re: how
References: <qHqKnNhkFFpow5Tl3Eiz12-8JEI@jntp> <daccd066-734a-4138-a64a-e0766e69eadf@att.net> <v26378$1q819$1@dont-email.me>
 <9310488b-e8c6-4ed8-913d-4abb7e241271@att.net> <t7-UZ1TyOKj1K2a2HoqROmxls_c@jntp>
 <08f3f962-d6b1-4f7c-b870-8cf29b85e2a7@att.net> <71YzuacI59BwfJhMavFstYgzlhs@jntp>
 <1e67c0e8-bf67-4d48-9896-57d429fd770c@att.net> <s0sZbdtbdzl3l1994GSDxosTxrc@jntp>
 <881f89fb-994d-4315-b134-4aec1576bca8@att.net>
Newsgroups: sci.math
JNTP-HashClient: ZBr__nmWKZEyBSSfbfBMlWWUdDQ
JNTP-ThreadID: 4YLc1knY-8u5i_KQ0oWqy89D7aY
JNTP-Uri: http://news2.nemoweb.net/?DataID=vol0FSJMuqv_Uox5qeHDiF8wsA4@jntp
User-Agent: Nemo/0.999a
JNTP-OriginServer: news2.nemoweb.net
Date: Tue, 21 May 24 16:55:21 +0000
Organization: Nemoweb
JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/124.0.0.0 Safari/537.36
Injection-Info: news2.nemoweb.net; posting-host="7a19405b4245f47946ffce65063ceb09f86be43b"; logging-data="2024-05-21T16:55:21Z/8867305"; 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: 2461
Lines: 33

Le 21/05/2024 à 17:50, Jim Burns a écrit :
> On 5/20/2024 4:08 PM, WM wrote:
>> Le 19/05/2024 à 22:28, Jim Burns a écrit :
> 
>>> Between each pair of unit fractions,
>>> there is a finite distance.
>>
>> Hence
>> not even two unit fractions
>> can satisfy the condition to
>> sit before any x > 0.
> 
> For any x > 0
> more.than.2 unit.fractions
> sit before x
> among them are ⅟⌊(1+⅟x)⌋ ⅟⌊(2+⅟x)⌋ ⅟⌊(3+⅟x)⌋

Of course, for any x that you can name, there are ℵo smaller unit 
fractions.
Ax_def > 0: NUF(x_def) = ℵo is right. 
> 
> zero unit fractions sit before any x > 0

So it is!
Therefore Ax > 0: NUF(x) = ℵo is wrong.

If you forget however to distinguish between x_def and x in general, you 
get the contradiction:

Ax > 0: NUF(x) = ℵo is wrong.
Ax > 0: NUF(x) = ℵo is right.
 
Regards, WM