Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Sun, 10 Nov 2024 12:20:06 +0200
Organization: -
Lines: 30
Message-ID: <vgq1cm$b5vj$1@dont-email.me>
References: <vg7cp8$9jka$1@dont-email.me> <0e67005f-120e-4b3b-a4d2-ec4bbc1c5662@att.net> <vga5mb$st52$1@dont-email.me> <vga7qi$talf$1@dont-email.me> <03b90d6c-fff1-411d-9dec-1c5cc7058480@tha.de> <vgb1fj$128tl$1@dont-email.me> <vgb2r6$11df6$3@dont-email.me> <vgcs35$1fq8n$1@dont-email.me> <vgfepg$22hhn$1@dont-email.me> <vgg0ic$25pcn$1@dont-email.me> <vggai3$25spe$8@dont-email.me> <vgi0t7$2ji2i$1@dont-email.me> <vgiet5$2l5ni$1@dont-email.me> <vgl2hj$3794c$1@dont-email.me> <vgleau$bi0i$2@solani.org> <vgnq3i$3qgfe$1@dont-email.me> <vgoka6$3vg2p$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sun, 10 Nov 2024 11:20:06 +0100 (CET)
Injection-Info: dont-email.me; posting-host="aa6135c12195030876f9317ea3566320";
	logging-data="366579"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+YTMqVEsCkvnooOTojfenb"
User-Agent: Unison/2.2
Cancel-Lock: sha1:iq3rL/TzqBUUhxHGq2kGH8y9Lt8=
Bytes: 2320

On 2024-11-09 21:30:47 +0000, WM said:

> On 09.11.2024 15:03, Mikko wrote:
>> On 2024-11-08 16:30:23 +0000, WM said:
> 
>>> 
>>> If Cantors enumeration of the rationals is complete, then all rationals
>>> are in the sequence 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 
>>> 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, 2/5, 3/4, 4/3, 5/2, 6/1,  ... and none is 
>>> outside.
>> 
>> All positive rationals quite obviously are in the sequence. Non-positive
>> rationals are not.
>> 
>>> Therefore also irrational numbers cannot be there.
>> 
>> That is equally obvious.
>> 
>>> Of course this is wrong.
>> 
>> You may call it wrong but that's the way they are.
> 
> The measure of all intervals J(n) = [n - √2/10, n + √2/10] is smaller than 3.

Maybe, maybe not, depending on what is all n. If all n is all reals then
the measure of their union is infinite.

-- 
Mikko