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RE: [Axiom-developer] StepThrough
From: |
Bill Page |
Subject: |
RE: [Axiom-developer] StepThrough |
Date: |
Fri, 4 Nov 2005 14:44:31 -0500 |
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
>
- Re: [Axiom-developer] was: Boot vs. Lisp / a smaller project, (continued)
- Re: [Axiom-developer] was: Boot vs. Lisp / a smaller project, Martin Rubey, 2005/11/02
- [Axiom-developer] StepThrough, C Y, 2005/11/02
- RE: [Axiom-developer] StepThrough, Bill Page, 2005/11/02
- RE: [Axiom-developer] StepThrough, C Y, 2005/11/02
- Re: [Axiom-developer] StepThrough, Martin Rubey, 2005/11/03
- RE: [Axiom-developer] StepThrough, Bill Page, 2005/11/04
- Re: [Axiom-developer] StepThrough, Martin Rubey, 2005/11/04
- Re: [Axiom-developer] StepThrough, C Y, 2005/11/04
- Re: [Axiom-developer] StepThrough, Bertfried Fauser, 2005/11/04
- RE: [Axiom-developer] StepThrough, Bill Page, 2005/11/04
- RE: [Axiom-developer] StepThrough,
Bill Page <=
- Re: [Axiom-developer] Live Pamphlet Editing, William Sit, 2005/11/05
- RE: [Axiom-developer] Live Pamphlet Editing, Bill Page, 2005/11/05
- RE: [Axiom-developer] Live Pamphlet Editing, Bill Page, 2005/11/05
- Re: [Axiom-developer] StepThrough, root, 2005/11/04
- Re: [Axiom-developer] StepThrough, C Y, 2005/11/05
- Re: [Axiom-developer] Units Package, William Sit, 2005/11/05
- [Axiom-developer] Re: StepThrough (was: Units package), Bill Page, 2005/11/05
- [Axiom-developer] Re: StepThrough (was: Units package), C Y, 2005/11/05
- [Axiom-developer] RE: StepThrough (was: Units package), Bill Page, 2005/11/05
- Re: [Axiom-developer] RE: StepThrough (was: Units package), root, 2005/11/05