Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Thu, 26 Dec 2024 05:09:44 +0100
Organization: A noiseless patient Spider
Lines: 23
Message-ID: <vkiku8$2pt4u$4@dont-email.me>
References: <vg7cp8$9jka$1@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>
 <d4d38bb75acc471a684759922b8f8d32707855a8@i2pn2.org>
 <vk6uu7$4f7v$1@dont-email.me>
 <cdd51ad73c172f40f3212801d7afd9eef8e60d47@i2pn2.org>
 <vk936n$khia$1@dont-email.me>
 <787067e5de3c455cb57389315b6821e96bcf86af@i2pn2.org>
 <f713f771-6cdd-44bb-90ab-7300d739f84b@tha.de>
 <1b6f89e7c35e4c9674af5a480e4bab6cb72e0915@i2pn2.org>
 <vkbalq$14tg7$2@dont-email.me>
 <733ce219e9d2422859035e5094a7b3e92eea9c47@i2pn2.org>
 <vke3bi$1q36j$2@dont-email.me>
 <md-cnZfuwoBJMPf6nZ2dnZfqnPGdnZ2d@giganews.com>
 <vkf5et$20tbj$1@dont-email.me>
 <BnWdnWn9ULkj0fb6nZ2dnZfqnPSdnZ2d@giganews.com>
 <vkikfn$2q3p8$1@dont-email.me>
Reply-To: invalid@example.invalid
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Thu, 26 Dec 2024 05:09:45 +0100 (CET)
Injection-Info: dont-email.me; posting-host="0c688897b869a728a98ca6eb2216ef6b";
	logging-data="2946206"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18EhcLFJHmegCBreivyUZpy"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:E/DRFnq8O8Ud28OmnbMYh2dhCog=
Content-Language: de-DE
In-Reply-To: <vkikfn$2q3p8$1@dont-email.me>
Bytes: 2630

Am 26.12.2024 um 05:02 schrieb Chris M. Thomasson:
> On 12/24/2024 4:07 PM, Ross Finlayson wrote:
>> On 12/24/2024 12:27 PM, Chris M. Thomasson wrote:

>>> Cantor's Pairing works with any unsigned integer.
>>
>> No, it works with two copies of all the integers, [...]
> 
> It works with any unsigned integer.

It works especially with the (elements in the) two sets {0, 2, 4, ...} 
and {1, 3, 5, ...}:

                   n <-> n+1 .

P := {(n, n+1) : n e {0, 2, 4, ...}} .

Then P is {(0, 1}, (2, 3}, (4, 5}, ...}.

..
..
..