On Wed, Feb 3, 2010 at 3:14 AM, Bruno Marchal <[email protected]> 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 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
