RE: [Axiom-developer] StepThrough

[Bill Page]

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
>