In article <87fvnm7q1n....@elektro.pacujo.net>, 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 âµâ bytes of RAM >>> and ran at âµâ 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 âµâ statements per second. That >doesn't guarantee a finite finish time but would make it possible. That >is because > > âµâ * âµâ = âµâ = âµâ * 1 > >This computer is definitely more powerful than a Turing machine, which >only has âµâ bytes of RAM and thus can't even store an arbitrary real >value in memory.
You're very much off the track here. A Turing machine is an abstraction for a computer were the limitations of size are gone. The most obvious feature of a Turing machine is an infinite tape. A Turing machine happily calculates Ackerman functions long after a real machine runs out of memory to represent it, with as a result a number of ones on that tape. But it only happens in the mathematicians mind. > > >Marko -- Albert van der Horst, UTRECHT,THE NETHERLANDS Economic growth -- being exponential -- ultimately falters. albert@spe&ar&c.xs4all.nl &=n http://home.hccnet.nl/a.w.m.van.der.horst
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