On Tue, Mar 5, 2019 at 4:55 PM Russell Standish <li...@hpcoders.com.au> wrote:
> On Tue, Mar 05, 2019 at 02:22:05PM +1100, Bruce Kellett wrote: > > On Tue, Mar 5, 2019 at 2:03 PM Russell Standish <li...@hpcoders.com.au> > wrote: > > > > You cannot represent n as a finite string for an arbitrary real > number > > n. But you can for an arbitrary integer n. > > > > > > Sure. But that was not part of your definition of a 'computation'. The > > algorithm f(x): (r-1)+1 works for all reals r as well as for finite > strings n. > > > > Bruce > > I don't think it's 'my definition'. The usual meaning of computable > integer is that there exists a program that outputs it. For real > numbers, this is changed to a program exists that outputs a sequence > of numbers that converges to the real number in question. One could > also consider "spigot" programs for this purpose too - a program that > outputs the decimal (or binary say) expansion of the real number. It > is clear that this more relaxed definition is equivalent to the former > in the integer case. > It seems that you are relying on the idea of 'computable' as capable of being calculated in a finite number of steps on a finite Turing machine. That is fine; it then rules out functions such as (r-1)+1 for reals, since these are not representable on a finite Turing machine. But it also renders the concept of a computable number completely trivial, and all you are left with for the Church-Turing thesis is the concept of computable functions which are non-trivial in the sense that the function cannot depend ab initio on the output number. Bruce -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
