Chris Angelico <ros...@gmail.com>: > 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: >> >> for x in continuum(0, max(1, y)): > > How exactly do you iterate over a continuum, with a digital computer?
How "digital" our idealized computers are is a matter for a debate. However, iterating over the continuum is provably "possible:" http://en.wikipedia.org/wiki/Transfinite_induction > 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. My assumption was you could execute ℵ₁ statements per second. That doesn't guarantee a finite finish time but would make it possible. That is because ℵ₁ * ℵ₁ = ℵ₁ = ℵ₁ * 1 This computer is definitely more powerful than a Turing machine, which only has ℵ₀ bytes of RAM and thus can't even store an arbitrary real value in memory. Marko -- https://mail.python.org/mailman/listinfo/python-list