Tom Caylor wrote:

>So apparently we are still missing something.  You need to tell us
>*why* this is not the right reason.  The set of instructions for g is
>precisely a big "case" statement (if you will) on n, like this:
>switch n:
>case 1:
>set of instructions for f1:
>case 2:
>set of instructions for f2:
>case 3:
>set of instructions for f3:
>end (after an infinite number of cases)
>This is an infinitely long program.  You need the whole program to
>define g, not just the portion you need for a given input.  Is there a
>finite version of g?  I don't see how.

I haven't been following the all details of this discussion, so apologies if 
I get things confused...but aren't those f1, f2, f3 etc. supposed to 
correspond *only* to turing machine programs which actually halt and give 
you a finite number as an output? If so, then although we can write down the 
list of all possible turing machine programs, there is no way to figure out 
which programs on this list correspond to one of your functions and which 
don't without solving the halting problem.


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