Re: HHH(DD) --- COMPUTE ACTUAL MAPPING FROM INPUT TO OUTPUT --- Using Finite String Transformations

Op 22.apr.2025 om 21:14 schreef olcott:

On 4/22/2025 1:10 PM, Fred. Zwarts wrote:

Op 22.apr.2025 om 18:38 schreef olcott:

>
a function is computable if there exists an algorithm
that can do the job of the function, i.e. given an input
of the function domain it can return the corresponding output.
https://en.wikipedia.org/wiki/Computable_function
>
On Turing Machines inputs <are> finite strings, and
finite string transformation rules <are> applied to
these finite strings to derive corresponding outputs.
>

And it has been proven that no finite string transformations are possible that report the halting behaviour for all inputs that specify a correct program.

 int sum(int x, int y) { return x + y; }
Only when people stupid assume the same thing as
sum(3,2) should return the sum of 5 + 3.
 

Therefore HHH should report on the actual input, the finite string that describes a halting program. Not on the hypothetical input that does not halt, because it is based on a hypothetical HHH that does not abort.
Why do you maintain that HHH should process the hypothetical input instead of the actual input.
Do you really believe that 3+2 equals 5+3?