Kevin Wampler wrote:
> `uninteresting' when you restrict yourself to a finite set of 
> *programs*, not functions.

Well, Rice's theorem, yes. I was speaking of mathematics in general.

> 2) I don't agree with your view on the use of infinity in mathematics. 
> On the contrary, infinity (or rather unboundedness, which I assume is 
> that you meant) is often used as a way to *simplify* things. 

Well, the existence of infinities in your inputs complicate things more than 
a system where everything is finite. A turing machine with a fixed-length 
tape is far less interesting to prove things about than otherwise.

Stuff like big-O notation only uses infinities because you're again assuming 
your functions have infinities in them. Every program on a finite machine 
finishes in O(1) time.

But yes, certainly I didn't mean to imply using infinities is always more 
complex than trying to avoid them in a problem where it's appropriate.

-- 
Darren New, San Diego CA, USA (PST)
   Serving Suggestion:
     "Don't serve this any more. It's awful."

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