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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 18:32:56 -0600
Organization: Christians and Atheists United Against Creeping Agnosticism
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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".

To understand what a halt decider does you need to first understand what 
the halting function is. And to understand that, you must first 
understand what a function is. You clearly do not.

André

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