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: > > On Tue, Mar 05, 2019 at 12:06:00PM +1100, Bruce Kellett wrote: > > > > My problem with your idea that the function: "(n-1)+1" is a valid > computational > > algorithm for n is that it makes all real numbers also computable, but > the > > notion of Turing computability applies only to the integers. We do not > want a > > definition of 'computable', that makes all reals computable. > > 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 is clear that all integers are computable according to the above, and that nearly all real numbers aren't (by virtue of there only being a countable number of programs). Cheers -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow hpco...@hpcoders.com.au Economics, Kingston University http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- 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.