On Thu, Feb 13, 2014 at 11:47 AM, Marko Rauhamaa <ma...@pacujo.net> wrote: > 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
You missed the most important point on that page, which is the "limit case". There is no way to iterate over all the reals one at a time, no matter how fast you execute instructions. If you could, it would be trivial to show that the reals have the same cardinality as the positive integers: correspond n with the whatever is returned by the nth call to it.next. It doesn't matter if you call your magical iterator "transfinite", that doesn't make it so. -- Devin -- https://mail.python.org/mailman/listinfo/python-list