On Wed, Feb 3, 2010 at 3:14 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:

>
> On 03 Feb 2010, at 03:00, Jason Resch wrote:
>
>  Is your point that with addition, multiplication, and an infinite number
> of successive symbols, any computable function can be constructed?
>
>
> You can say so.
> You could also have said that with addition + multiplication *axioms* + *
>  logic*, any computable function can be proved to exist.
>
>
>
So I suppose that is what I was wondering, given at minimum, those, how is
the existence of a computable function proved to exist?  Could you provide
an example of how a simple function, like f(x) = x*2 exists, or is it a very
tedious proof?



>
> Or do the relations imposed by addition and multiplication somehow create
> functions/machines?
>
>
> You can say so but you need logic. Not just in the (meta) background, but
> made explicit in the axiom of the theory, or the program of the machine
> (theorem prover).
>
>
>
>
> Thanks,
>
>
> You are welcome. Such questions help to see where the difficulties remain.
> Keep asking if anything is unclear.
>
>
>
Thanks again, things are becoming a little more clear for me.  My background
is in computer science, in case that applies and helps in writing an
explanation for my question above.

Jason

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