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.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Fri, 20 Dec 2024 22:37:59 -0500
Organization: i2pn2 (i2pn.org)
Message-ID: <d4d38bb75acc471a684759922b8f8d32707855a8@i2pn2.org>
References: <vg7cp8$9jka$1@dont-email.me>
 <c6b624cb0b1b55d54aab969ee5b4e283ec7be3cd@i2pn2.org>
 <vjhp8b$3gjbv$1@dont-email.me>
 <dc9e7638be92c4d158f238f8c042c8559cd46521@i2pn2.org>
 <vjjg6p$3tvsg$1@dont-email.me>
 <c31edc62508876748c8cf69f93ab80c0a7fd84ac@i2pn2.org>
 <vjka3b$1tms$3@dont-email.me>
 <e11a34c507a23732d83e3d0fcde7b609cdaf3ade@i2pn2.org>
 <vjmse3$k2go$2@dont-email.me>
 <069069bf23698c157ddfd9b62b9b2f632b484c40@i2pn2.org>
 <vjooeq$11n0g$2@dont-email.me>
 <2d3620a6e2a8a57d9db7a33c9d476fe03cac455b@i2pn2.org>
 <vjrfcc$1m1b2$1@dont-email.me>
 <3c08ed64fa6193dc9ab6733b807a5c99a49810aa@i2pn2.org>
 <vjss56$1tr00$2@dont-email.me>
 <357a8740434fb6f1b847130ac3afbd33c850fc37@i2pn2.org>
 <vjv6fb$2dujf$2@dont-email.me>
 <b0c7449413fec43bc18e8d2d67da1c779a350bc2@i2pn2.org>
 <vk1cad$2srst$1@dont-email.me>
 <ceaaf003457afd2e381c8f115a4e691611162ffe@i2pn2.org>
 <vk3g0l$3cjvc$3@dont-email.me> <vk3lv1$3e9se$1@dont-email.me>
 <vk3vh6$3g0a3$1@dont-email.me> <vk4jfi$3k04r$4@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sat, 21 Dec 2024 03:37:59 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="3884300"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
X-Spam-Checker-Version: SpamAssassin 4.0.0
In-Reply-To: <vk4jfi$3k04r$4@dont-email.me>
Content-Language: en-US
Bytes: 2964
Lines: 27

On 12/20/24 3:18 PM, Chris M. Thomasson wrote:
> On 12/20/2024 6:38 AM, WM wrote:
>> On 20.12.2024 12:55, Chris M. Thomasson wrote:
>>> On 12/20/2024 2:13 AM, WM wrote:
>>>> On 20.12.2024 03:52, Richard Damon wrote:
>>>>
>>>>> He builds an infinite sequence that pairs a natural number to every 
>>>>> rational number .
>>>>
>>>> And I build an infinite sequence of intervals [1, n] that contains 
>>>> every natural number.
>>>
>>> Cantor Pairing works will any of them.
>>
>> Therefore no interval [1, n] and therefore no n is missing in my proof 
>> that the pairing
>> 10n --> n, n ∈ ℕ
>> does not work. For every interval at least 9/10 are missing.
> 
> Huh? Have you ever implemented Cantor Pairing and tried it out? It works 
> with any unsigned integer. So, it works with all of them. Why do you 
> seem to have trouble with it?

His problem is he isn't using the actual set of Natural Numbers, only a 
FISON of 1 to n, and thus a lot of the numbers don't have the needed 
10xn available.