Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Sun, 10 Nov 2024 12:34:53 -0800
Organization: A noiseless patient Spider
Lines: 16
Message-ID: <vgr5dc$i3h7$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me>
 <0e67005f-120e-4b3b-a4d2-ec4bbc1c5662@att.net> <vgab11$st52$3@dont-email.me>
 <ecffc7c0-05a2-42df-bf4c-8ae3c2f809d6@att.net> <vgb0ep$11df5$4@dont-email.me>
 <35794ceb-825a-45df-a55b-0a879cfe80ae@att.net> <vgfgpo$22pcv$1@dont-email.me>
 <40ac3ed2-5648-48c0-ac8f-61bdfd1c1e20@att.net> <vgg57o$25ovs$2@dont-email.me>
 <71fea361-0069-4a98-89a4-6de2eef62c5e@att.net> <vggh9v$27rg8$3@dont-email.me>
 <ff2c4d7c-33b4-4aad-a6b2-88799097b86b@att.net> <vghuoc$2j3sg$1@dont-email.me>
 <d79e791d-d670-4a5a-bd26-fdf72bcde6bc@att.net> <vgj4lk$2ova9$3@dont-email.me>
 <f154138e-4482-4267-9332-151e2fd9f1ba@att.net> <vgkoi7$b5pp$1@solani.org>
 <d780ead415ff3a62ccd9b606bcd743fea3d8002c@i2pn2.org>
 <vglf32$396r8$1@dont-email.me>
 <521668acd2ed6184f2f2e36f67fdb1bc3a997524@i2pn2.org>
 <vglslt$3bl8n$1@dont-email.me> <vglso1$3bl8n$2@dont-email.me>
 <vgokv7$n50i$1@solani.org> <vgol5o$3vr0c$1@dont-email.me>
 <vgom45$3vvgt$1@dont-email.me> <vgptpa$aeoa$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Sun, 10 Nov 2024 21:34:53 +0100 (CET)
Injection-Info: dont-email.me; posting-host="2f6d4651da9b9d481a89da3e4ea06f77";
	logging-data="593447"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19qsttzuA9XfjWAh7P26XLWY/Mefnk7q5Y="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:mh2SkoxFMwuFDyYrcf5zQ/L6ygo=
In-Reply-To: <vgptpa$aeoa$1@dont-email.me>
Content-Language: en-US
Bytes: 2714

On 11/10/2024 1:18 AM, WM wrote:
> On 09.11.2024 23:01, Moebius wrote:
> 
>> It confirms only that both sets have the same size, actually aleph_0.
> 
> True but irrelevant. For covering of all rationals by all naturals there 
> must be the same reality, but that is not.

Did you know that Cantor pairing can turn any natural number into a 
_unique_ pair of natural numbers? This unique pair can be turned back 
into the original natural number. It's a mapping at its essence. 
Actually, it can be used for hashing, anyway...

The original natural number is there. The pair of natural numbers is 
also there. We can go back and forth between them? They are all there in 
the infinite set of natural numbers!