Path: ...!2.eu.feeder.erje.net!3.eu.feeder.erje.net!feeder.erje.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Mon, 9 Sep 2024 17:15:23 +0200
Organization: A noiseless patient Spider
Lines: 17
Message-ID: <vbn3eb$2em18$4@dont-email.me>
References: <vb4rde$22fb4$2@solani.org>
 <0da78c91e9bc2e4dc5de13bd16e4037ceb8bdfd4@i2pn2.org>
 <vb57lf$2vud1$1@dont-email.me> <5d8b4ac0-3060-40df-8534-3e04bb77c12d@att.net>
 <vb6o0r$3a4m1$2@dont-email.me> <7e1e3f62-1fba-4484-8e34-6ff8f1e54625@att.net>
 <vbabbm$24a94$1@solani.org> <06ee7920-eff2-4687-be98-67a89b301c93@att.net>
 <38ypmjbnu3EfnKYR4tSIu-WavbA@jntp>
 <34e11216-439f-4b11-bdff-1a252ac98f8f@att.net> <vbd56i$fqa0$1@dont-email.me>
 <vbdbq3$gdoe$2@dont-email.me> <vbes57$qdqo$2@dont-email.me>
 <27b3b5e088d82d4475c68a64f50a4bccac9c6f29@i2pn2.org>
 <vbesjo$27gfe$1@solani.org> <vbf0s9$qp1j$3@dont-email.me>
 <vbfpf5$utdu$2@dont-email.me> <vbh5qe$19a45$1@dont-email.me>
 <vbhdf6$1btm1$1@dont-email.me> <vbhffg$1bi3l$3@dont-email.me>
 <035b16b56a204dfe5e561b3cfe03238167dba39a@i2pn2.org>
 <vbhiv7$1bi3k$1@dont-email.me> <vbhmj4$1cg6l$4@dont-email.me>
 <vbkttc$20uoj$3@dont-email.me> <vbl1nq$21t3j$3@dont-email.me>
 <vbmi4b$2ce0a$1@dont-email.me> <vbn0tb$2d8fc$6@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 09 Sep 2024 17:15:24 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="cd14fc04a24dd051d3dbc2b7b6e5cc4c";
	logging-data="2578472"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX198mwgQmmsrdoT74E0YQ9bmPDhtooNRDT0="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:qMwqX3bIdTl/2kmq7iLLJk+ItgI=
Content-Language: en-US
In-Reply-To: <vbn0tb$2d8fc$6@dont-email.me>
Bytes: 2743

On 09.09.2024 16:32, Python wrote:
> Le 09/09/2024 à 12:19, Prof. Dr. Mückenheim, aka WM a écrit :

>> ℵo unit fractions cannot fit into one of the ℵo intervals 
>> between two of them.
> 
> (O, x) is NOT an interval between two unit fractions.

1/n - 1/(n+1) = x is an interval between two unit fraction. This 
interval is shifted to the origin, yielding the interval (0, x). It does 
not contain ℵo unit fractions. It does not contain 1/n.

Note that unit fractions are points on the real line. Therefore there is 
a beginning. How many unit fractions can be smallerorequal than all unit 
fractions. This question proves the existence of a smallest unit fraction.

Regards, WM