Oscar Benjamin <oscar.j.benja...@gmail.com>: > This isn't even a question of resource constraints: a digital computer > with infinite memory and computing power would still be limited to > working with countable sets, and the real numbers are just not > countable. The fundamentally discrete nature of digital computers > prevents them from being able to truly handle real numbers and real > computation.
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 The function could well return in finite time with a precise result for any given nonnegative real argument. Marko -- https://mail.python.org/mailman/listinfo/python-list