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

On 5/1/25 10:25 PM, olcott wrote:

On 5/1/2025 9:10 PM, André G. Isaak wrote:

On 2025-05-01 19:55, olcott wrote:
>

Specify every single step of the mapping and you will
see that it has never been well defined. It has ONLY
ever been a leap to a conclusion.

>
Mappings don't HAVE steps. Again, you are confusing functions with algorithms.
>
André
>

 In other words people just guess that a mapping exists or not?
THE MAPPING FROM INPUTS TO OUTPUTS IS BY FINITE STRING TRANSFORMATIONS.

No, the computation is by a finite algorithm of finite string operations.
The mapping is a mapping from one object to another.
We CAN define a transformation (it isn't based on a finite algorithm) that says map string x to the halting status of the direct execution of the program that x represents.
That *IS* a transformation of finite strings. It is just not a transformation based on a finite algorithm.

 The mapping to compute the sum function is from integers
transformed by the steps of arithmetic to an integer OUTPUT.

So, that particular mapping can be defined in terms of operations

 int sum(int x, int y) { return 5; }
The above mapping IS NOT for the sum function.
 

An no one said it was.
They said that it was a computation that computed a function that correctly answered the question of sum(3, 2) which is 5.
You are just showing your lack of reading comprehension.