Path: ...!eternal-september.org!feeder3.eternal-september.org!news.quux.org!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Thu, 10 Apr 2025 21:27:21 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <6ce86dfd0bce01ed28b84f47d243cc1bc5365d75@i2pn2.org>
References: <vsn1fu$1p67k$1@dont-email.me> <vsng73$27sdj$1@dont-email.me>
 <gGKdnZiYPJVC03L6nZ2dnZfqn_udnZ2d@brightview.co.uk>
 <vsnk2v$2fc5a$1@dont-email.me> <vsnmtg$2i4qp$3@dont-email.me>
 <vsno7m$2g4cd$3@dont-email.me> <vsnp0o$2ka6o$2@dont-email.me>
 <vsnpv4$2g4cd$6@dont-email.me> <vsntes$2osdn$1@dont-email.me>
 <vsntv3$2paf9$1@dont-email.me> <vso1a0$2sf7o$1@dont-email.me>
 <vso2ff$2tj1d$2@dont-email.me> <vso3rj$2vems$2@dont-email.me>
 <vso4gh$2vg3b$1@dont-email.me> <vsqmlb$1ktm5$6@dont-email.me>
 <vsr1ae$1pr17$2@dont-email.me> <vst4nm$8daf$2@dont-email.me>
 <vst8ci$aeqh$3@dont-email.me> <vsutjt$21mp2$2@dont-email.me>
 <vsuvp1$227l5$1@dont-email.me> <vsvv3h$36pju$2@dont-email.me>
 <vt01u5$38f07$1@dont-email.me> <875xjfd5rs.fsf@nosuchdomain.example.com>
 <vt1jpa$n43m$4@dont-email.me> <87tt6zblzl.fsf@nosuchdomain.example.com>
 <0920ac6e196c1cebeff36d8b9431ee12a7b3d527@i2pn2.org>
 <vt74k1$1pl6i$5@dont-email.me> <vt7sgd$2ht4t$1@dont-email.me>
 <vt9nq3$5t7s$4@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Fri, 11 Apr 2025 01:27:22 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="4021561"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
X-Spam-Checker-Version: SpamAssassin 4.0.0
Content-Language: en-US
In-Reply-To: <vt9nq3$5t7s$4@dont-email.me>
Bytes: 3113
Lines: 27

On 4/10/25 8:29 PM, Lawrence D'Oliveiro wrote:
> On Thu, 10 Apr 2025 10:37:49 +0300, Mikko wrote:
> 
>> On 2025-04-10 00:50:10 +0000, Lawrence D'Oliveiro said:
>>
>>> On Mon, 7 Apr 2025 20:48:27 -0400, Richard Damon wrote:
>>>
>>>> The paper clearly talks about the process continuing indefinitely.
>>>
>>> Note the key point about any computation of a computable number is that
>>> the answer *converges* to the exact result in the limit. As you compute
>>> more and more digits, the discrepancy between your approximation and
>>> the correct answer can be made as close to zero as you like, just as
>>> long as you don’t ask for it to be zero.
>>>
>>> The Cantor construction does not converge.
>>
>> If it is a computable number it does converge.
> 
> That’s a key point of my proof: if it converges, then the number is
> already in the list. The only way it can come up with a number not in the
> list is by never converging.

it doesn't need to not converge, it just has to be different from every 
other number on the list, since he was just showing uncountable.

Since it is different from the list of every contable number, it must be 
part of a larger set, and uncntable infinity.