Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions apply finite string
 transformations to inputs +++
Date: Mon, 28 Apr 2025 21:21:32 +0100
Organization: Fix this later
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In-Reply-To: <vuomum$2gnd$1@dont-email.me>

On 28/04/2025 21:03, olcott wrote:
> On 4/28/2025 2:58 PM, dbush wrote:

<snip>

>> Category error.  The halting function below is fully defined, 
>> and this mapping is not computable *as you have explicitly 
>> admitted*.
>>
> 
> Neither is the square root of an actual onion computable.
> 
> Turing Computable Functions are required to apply finite
> string transformations to their inputs. The function defined
> below ignores that requirement PROVING THAT IT IS INCORRECT.

No, it proves that you agree that it's not a computable function. 
QED.

>> Given any algorithm (i.e. a fixed immutable sequence of 
>> instructions) X described as <X> with input Y:
>>
>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when 
>> executed directly


-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within