markh@csd4.csd.uwm.edu (Mark William Hopkins) (04/29/91)
In article <4026@bruce.cs.monash.OZ.AU> mmcg@bruce.cs.monash.OZ.AU (Mike McGaughey) writes: >Yes. Pick any famous unsolved mathematical theorem, and try to solve >it by brute force - i.e. prove that this one terminates: > >read x >while (x > 1) > if x mod 2 = 0 then > x = x / 2 > else > x = 3 * x + 1 Actually, there is a relatively simple proof that uses the irrationality of log(3)/log(2), but unfortunately I haven't the time to go into it: our system's gonna go down and I have to finish some major projects. :) :) Play around with the function f(1) = 0 f(2n) = f(n) + 1 f(2n + 1) = f(3n + 2) + 2 for a while. Maybe you'll see it...