Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Sun, 15 Dec 2024 12:50:20 +0200
Organization: -
Lines: 25
Message-ID: <vjmc9c$hl7j$2@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me> <vg7vgh$csek$1@dont-email.me> <vg8911$dvd6$1@dont-email.me> <vjgvpc$3bb3f$1@dont-email.me> <vjh28r$3b6vi$4@dont-email.me> <vjjfmj$3tuuh$1@dont-email.me> <vjjgds$3tvsg$2@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sun, 15 Dec 2024 11:50:21 +0100 (CET)
Injection-Info: dont-email.me; posting-host="548af6b5414b171555f35e270ee8ad08";
	logging-data="578803"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+XCWCCBJh8fwUOjoWCnCEM"
User-Agent: Unison/2.2
Cancel-Lock: sha1:2KndPnj/eSwzkudnuEYQutl4DGM=
Bytes: 1841

On 2024-12-14 08:42:37 +0000, WM said:

> On 14.12.2024 09:30, Mikko wrote:
>> On 2024-12-13 10:28:44 +0000, WM said:
>> 
>>> On 13.12.2024 10:46, Mikko wrote:
>>> 
>>>> Between any two intervals there is space and that space contains other
>>>> intervals.
>>> 
>>> No. Starting from a point in the complement the cursor will hit a first 
>>> interval. This is true for all visible intervals.
>> 
>> False. From a point that is not a part of an interval no interval is the
>> nearest one because another interval is nearer.
> 
> IF ALL intervals and their endpoints are existing as invariable points 
> on the real line this cannot happen.

It can. Your { [q_n - sqrt(2)/2^n, q_n + sqrt(2)/2^n] | n = 1, 2, 3, ... }
is one such set.

-- 
Mikko