Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Sun, 15 Dec 2024 07:52:11 -0500
Organization: i2pn2 (i2pn.org)
Message-ID: <226bc62e19a54dd1daece7527c572801b6fd9d39@i2pn2.org>
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$2@dont-email.me> <vjmc9c$hl7j$2@dont-email.me>
 <vjmdbt$hn65$3@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Sun, 15 Dec 2024 12:52:11 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="2973922"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
In-Reply-To: <vjmdbt$hn65$3@dont-email.me>
Content-Language: en-US
X-Spam-Checker-Version: SpamAssassin 4.0.0
Bytes: 2436
Lines: 36

On 12/15/24 6:08 AM, WM wrote:
> On 15.12.2024 11:50, Mikko wrote:
>> 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.
> 
> That is nothing but an unfounded claim. In actual infinity of set theory 
> all intervals and their endpoints are existing as invariable points from 
> the beginning of the cursor's motion.
> 
> Regards, WM
> 
> 

So? The problem is the cursor can't move without immediately hitting 
segments, none of which are "next" because they are dense.