10/10/2009, 01:05 AM
So then you got it via the scientific process -- you first hypothesized that it should decay to a fixed point, as that would be a simple type of behavior. Then combined with the postulate of the holomorphism, the tetrational can be recovered via the Cauchy integral. And that provides a test: construct it via the integral given the supposed behavior, and see what happens. And the test was done, and it worked. So now as this is mathematics, I guess the next step would be the formal proof of the existence and uniqueness of the solution.