Path: ...!weretis.net!feeder8.news.weretis.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: Fri, 20 Sep 2024 20:24:14 +0200
Organization: A noiseless patient Spider
Lines: 33
Message-ID: <vckekf$1709o$1@dont-email.me>
References: <vb4rde$22fb4$2@solani.org> <vbnuqq$2it4a$2@dont-email.me>
 <vbp9dk$2u3sh$1@dont-email.me> <vbq4ve$31fu6$10@dont-email.me>
 <fd09e9afa6b0c3041b90c5d788681bb2c92f9d2e@i2pn2.org>
 <vbs9v8$3l368$3@dont-email.me>
 <405557f7289631d63264c712d137244c940b9926@i2pn2.org>
 <vbsroa$3mvi7$2@dont-email.me> <vbt0fs$3pr1d$1@dont-email.me>
 <vbt15n$3qapk$1@dont-email.me> <btbO__HYVIMPfoOcmXp4_whV8-8@jntp>
 <vbums6$8kdn$1@dont-email.me> <vbv9i7$bpjh$2@dont-email.me>
 <13c08e96ad635f8142b38d89863a80caf17a32a8@i2pn2.org>
 <vc1mfe$u3ec$2@dont-email.me>
 <4faa63d0ff8c163f01a38736aeb5732184218a29@i2pn2.org>
 <vc1uu8$u3ec$9@dont-email.me> <vc2gfb$130uk$1@dont-email.me>
 <vc44uu$1gc40$1@dont-email.me>
 <c94d6140f000f75c5e95e1acc785ebff9894a18b@i2pn2.org>
 <vc7dk3$2b1g9$2@dont-email.me> <1aabd037-86bc-47bd-b402-f6b29c5c33e4@att.net>
 <vcehl6$2boc$3@dont-email.me> <f1d14b16-2c12-4cfb-b7f5-c58cc5724f94@att.net>
 <vcguvh$hi5j$1@dont-email.me> <b7eb4682-30db-4b37-90b4-0135e995cfc1@att.net>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Fri, 20 Sep 2024 20:24:15 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="1061d01a4cfe8348dd8e8a6228956824";
	logging-data="1278264"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1/tLFWxRbDj6Mn9QrXyTwvpgxMF9sRcgi8="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:Our02lLDFbpcEli1nvNBik83VmE=
Content-Language: en-US
In-Reply-To: <b7eb4682-30db-4b37-90b4-0135e995cfc1@att.net>
Bytes: 2747

On 19.09.2024 20:31, Jim Burns wrote:
> On 9/19/2024 6:38 AM, WM wrote:

>> Either there is a point next to zero
>> or there is no point next to zero,
> 
> Consider ABCDEFGHIJKLMNOPQRSTUVWXYZ
> 
> Q is between A and Z
> A and Z are not next to each other.
> 
> Nothing is between P and Q
> P and Q are next to each other.
> 
> ⎛ There is a gap between P and Q

No.

> ⎜ A gap isn't some _presence_
> ⎜ A gap is an _absence_ of whatever.

A gap in the real line is the absence of points.

> Consider the real line.
> For any two points x and y,
> (x+y)/2 is between x and y.
> x and y are not next to each other.

That is true for definable points only.

Regards, WM
>