Path: ...!eternal-september.org!feeder3.eternal-september.org!i2pn.org!i2pn2.org!.POSTED!not-for-mail
From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Tue, 8 Apr 2025 18:59:02 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <9c010b974bc63471bf86d7c0631f2ea0af450007@i2pn2.org>
References: <vsn1fu$1p67k$1@dont-email.me>
 <7EKdnTIUz9UkpXL6nZ2dnZfqn_ednZ2d@brightview.co.uk>
 <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$6@dont-email.me>
 <vstl33$p9c2$1@dont-email.me> <vstme2$n9gi$2@dont-email.me>
 <HMScneI80ehcN2_6nZ2dnZfqn_SdnZ2d@brightview.co.uk>
 <vsuc78$1f8in$1@dont-email.me>
 <356fe829b105738f556ce1f89999ae620dcd2071@i2pn2.org>
 <vsvv9d$36pju$4@dont-email.me>
 <6ec3f1fc01602ad5305acdddfb0234d561ed9ffd@i2pn2.org>
 <vt432h$32bmm$2@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 8 Apr 2025 22:59:38 -0000 (UTC)
Injection-Info: i2pn2.org;
	logging-data="3721402"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg";
User-Agent: Mozilla Thunderbird
Content-Language: en-US
In-Reply-To: <vt432h$32bmm$2@dont-email.me>
X-Spam-Checker-Version: SpamAssassin 4.0.0
Bytes: 2717
Lines: 20

On 4/8/25 5:05 PM, Lawrence D'Oliveiro wrote:
> On Mon, 7 Apr 2025 06:47:43 -0400, Richard Damon wrote:
> 
>> And an infinite listing of values doesn't need to be computable, even if
>> every number in the list is computable.
> 
> Computability is a characteristic of particular numbers. It is a
> characteristic of all the numbers in the list, and of the number that the
> Cantor construction tries to construct from those numbers in the list.
> 
> The fact that you can’t apply that characteristic to the set as a whole is
> irrelevant, since the set itself is not a number.

Right, so the DIAGONAL number, which you claim to be computable, needs a 
finite algorithm to do so.

The algorithm described is NOT FINITE, as it includes the infinite 
number of algorithms to compute all the other numbers.

The problem is the list of numbers it is using is infinite, so the list 
of algorithms is also, so can't be held in a finite algorithm.