On Fri, Feb 14, 2014 at 1:00 AM, Marko Rauhamaa <ma...@pacujo.net> wrote: > Well, if your idealized, infinite, digital computer had ℵ₁ bytes of RAM > and ran at ℵ₁ hertz and Python supported transfinite iteration, you > could easily do reals: > > def real_sqrt(y): > for x in continuum(0, max(1, y)): > # Note: x is not traversed in the < order but some other > # well-ordering, which has been proved to exist. > if x * x == y: > return x > assert False
How exactly do you iterate over a continuum, with a digital computer? Even adding to your requirements that it have an ℵ₁ Hz bus (which, by the way, I *totally* want - the uses are endless), it would take a finite amount of time to assign to x the "next number", ergo your algorithm can't guarantee to finish in finite time. ChrisA -- https://mail.python.org/mailman/listinfo/python-list