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From: =?UTF-8?B?QW5kcsOpIEcuIElzYWFr?= <agisaak@gm.invalid>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions MUST apply finite string
 transformations to inputs
Date: Thu, 1 May 2025 19:58:31 -0600
Organization: Christians and Atheists United Against Creeping Agnosticism
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In-Reply-To: <vv160a$3smj7$1@dont-email.me>

On 2025-05-01 19:09, olcott wrote:
> On 5/1/2025 7:32 PM, André G. Isaak wrote:
>> On 2025-05-01 14:15, olcott wrote:
>>> On 5/1/2025 10:14 AM, André G. Isaak wrote:
>>>> On 2025-04-30 21:50, olcott wrote:
>>>>> On 4/30/2025 7:17 PM, André G. Isaak wrote:
>>>>
>>>>>> You are still hopelessly confused about your terminology.
>>>>>>
>>>>>> Computable functions are a subset of mathematical functions, and 
>>>>>> mathematical functions are *not* the same thing as C functions. 
>>>>>> Functions do not apply "transformations". They are simply 
>>>>>> mappings, and a functions which maps every pair of natural numbers 
>>>>>> to 5 is a perfectly legitimate, albeit not very interesting, 
>>>>>> function.
>>>>>>
>>>>>> What makes this function a *computable function* is that fact that 
>>>>>> it is possible to construct a C function (or a Turing Machine, or 
>>>>>> some other type of algorithm) such as int foo(int x, int y) 
>>>>>> {return 5;} which computes that particular function; but the C 
>>>>>> function and the computable function it computes are entirely 
>>>>>> separate entities.
>>>>>
>>>>> computes the sum of two integers
>>>>> by transforming the inputs into an output.
>>>>> int sum(int x, int y) { return x + y; }
>>>>>
>>>>> Computes no function because it ignores its inputs.
>>>>> int sum(int x, int y) { return 5; }
>>>>
>>>> All you're demonstrating here is that you have no clue what a 
>>>> function is, nor, apparently, do you have any desire to learn.
>>>>
>>>> André
>>>>
>>>
>>> What I am explaining is that a halt decider
>>> must compute the mapping FROM THE INPUTS ONLY
>>> by applying a specific set of finite string
>>> transformations to the inputs.
>>
>> No. Halt deciders weren't even mentioned above. I was addressing your 
>> absurd claim that int foo(int x, int y) { return 5; } does not compute 
>> a function. This clearly indicates that you do not grasp the concept 
>> of "function".
>>
> 
> This is a brand new elaboration of computer
> science that I just came up with.

IOW something you've pulled out of your ass.

> It is common knowledge THAT inputs must correspond
> to OUTPUTS. What is totally unknown and brand new
> created by me is HOW inputs are made to correspond
> to OUTPUTS.

We were discussing functions. Functions don't have inputs or outputs; 
they have domains and codomains. ALGORITHMS have inputs and outputs, and 
you keep conflating the two.

> Specific finite string transformation rules are
> applied to inputs to derive outputs.

Please point to a definition of 'function' which mentions "finite string 
transformation rules". This may be a useful way of viewing some (but 
certainly not all) algorithms, but it has nothing to do with functions. 
Functions are simply a mapping from one set (the domain) to another set 
(the codomain) such that every element of the domain maps to one and 
only one element of the codomain.

> What everyone else has been doing is simply GUESSING
> that they correspond or relying on some authority
> that say they must correspond. (Appeal to authority error).

This is another baseless assertion that you've simply pulled out of your 
ass. If you think otherwise, please provide a concrete example

> DD correctly emulated by HHH maps to NON-HALTING BEHAVIOR.
> It really does, all that you have to do is PAY ATTENTION.

Whether DD emulated by HH maps to halting or non-halting behaviour is 
entirely dependent on which function is being computed.

André

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