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: Mon, 16 Dec 2024 18:55:56 -0500
Organization: i2pn2 (i2pn.org)
Message-ID: <29a5ba6b377b4d0830915bff47f2560dfbfb63da@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>
 <539edbdf516d69a3f1207687b802be7a86bd3b48@i2pn2.org>
 <vjk97t$1tms$1@dont-email.me> <vjmc7h$hl7j$1@dont-email.me>
 <vjmd6c$hn65$2@dont-email.me>
 <cdf0ae2d3923f3b700a619a16975564d95d38370@i2pn2.org>
 <vjnaml$n89f$1@dont-email.me>
 <75dbeab4f71dd695b4513627f185fcb27c2aaad1@i2pn2.org>
 <vjopub$11n0g$5@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Mon, 16 Dec 2024 23:55:57 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="3216529"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
Content-Language: en-US
X-Spam-Checker-Version: SpamAssassin 4.0.0
In-Reply-To: <vjopub$11n0g$5@dont-email.me>
Bytes: 2292
Lines: 22

On 12/16/24 3:55 AM, WM wrote:
> On 15.12.2024 22:14, Richard Damon wrote:
>> On 12/15/24 2:29 PM, WM wrote:
> 
>>> Next is a geometric property, in particular since the average 
>>> distance of intervals is infinitely larger than their sizes.
> 
>> Not sure where you get that the "average" distance of intervals is 
>> infinitely larger than ther sizes.
> 
> The accumulated size of all intervals is less than 3 over the infinite 
> length. Hence there is at least one location with a ratio oo between 
> distance to the interval and length of the interval. Start there with 
> the cursor. It will hit one next interval. Crash.
> 
> Regards, WM

Since none of the gaps are infinte, and none of the intervals are of 0 
size, there is no "infinite" ratio of any gap to any interval.

Your logic is just broken.