Roger Hui <[email protected]> wrote: > Well, what's a computation? Is y=x a computation, where x is a number, > including an irrational?
Such a computation would require an infinite input tape (to specify the irrational), which isn't considered a computation. > I thought we were talking about mathematical > numbers? A computation in the sense of the ultimate result of a Turing machine -- the final tape produced after the machine halts (or the limit of the tape at infinity, which would allow for transcendental numbers to result from non-halting computations). As I mentioned, this result is accepted as proven by the mathematical community -- there are only finitely many numbers that can result from computation, even using an infinite number of steps. > Proof of my other assertions: Your other claim seems to me to be correct. -Wm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
