Re: Turing Machine computable functions MUST apply finite string transformations to inputs

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
--
To email remove 'invalid' & replace 'gm' with well known Google mail service.