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

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.
int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
Everyone assumes that it is correct to ignore
the required finite string transformations
that mandate DD correctly emulated by HHH
cannot possibly reach its own final halt state
no matter what of an infinite set of HHH's does.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer