On November 4, 2005 2:32 PM I wrote: > > > > You can algebraically define %pi and %e, of course you cannot > > give a digital or decimal presentations, but would that be > > desirable? %pi is fine for me ;-) > > This is not a matter of algebraic definition. Yes you can give > a digital representation. The thing is, it is just not finite. > The essence of the idea of exact real numbers is that it is > possible to finitely encode an algorithm which will compute > %pi (or any other "computable" real number) as an infinite stream > of digits. In any given computation though one does need the > entire infinite stream. Still one can treat the algorithm itself > as the representation of such a number. >
I meant to write: "In any given computation though one does *not* need the entire infinite stream." > This has been studied in some detail and there are some proposed > efficient implementations. Please see the "Some History" section > of: > > http://wiki.axiom-developer.org/RealNumbers > _______________________________________________ Axiom-developer mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-developer
