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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Cantor Diagonal Proof
Date: Thu, 10 Apr 2025 21:21:18 -0400
Organization: i2pn2 (i2pn.org)
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On 4/10/25 8:28 PM, Lawrence D'Oliveiro wrote:
> On Wed, 9 Apr 2025 22:00:11 -0400, Richard Damon wrote:
> 
>> On 4/9/25 8:41 PM, Lawrence D'Oliveiro wrote:
>>>
>>> On Tue, 8 Apr 2025 18:57:17 -0400, Richard Damon wrote:
>>>
>>>> The problem is your "master" algorithm need the algorithms of *ALL*
>>>> the computable numbers within it, which is an infinite number of
>>>> algorithms, and thus isn't itself a finite algorithm.
>>>
>>> That is the problem with the Cantor construction, not with my disproof
>>> of it. My disproof of it only needs a finite number of list elements at
>>> any point in the proof. The Cantor construction needs them all.
>>
>> But a finite list can't get you to the needed arbitrary precision
>> needed.
> 
> I was going to say, sure it can, because the size of the list is a
> function of the precision you ask for.

But the function needs to be prepared to handle ANY precision, and thus 
needs to be infinite.


> 
> But that’s irrelevant, because if you’re saying an infinite list cannot be
> constructed, then that blows the Cantor construction out of the water,
> since an infinite list is precisely what it assumes.

But Cantor wasn't talking about "Construction" in that manner, as he 
wasn't talking about computability.

He was describing a method for a ideal infinite logic to create the value.

> 
>> Not also, Cantor only claimed that the numbers weren't countable, he
>> didn't talk about computable. That is a later work looking at the proof.
> 
> True. But interesting things happen when you try to apply his construction
> to other kinds of number lists.

But you need to remember that he wasn't "constructing" it in the manner 
you are assuming, it isn't being constructed by a finite function, as 
that wasn't the domain he was talking about.