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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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