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## [Axiom-developer] [#167 Infinite Floats Domain] That's cool but ...

**From**: |
Bill Page |

**Subject**: |
[Axiom-developer] [#167 Infinite Floats Domain] That's cool but ... |

**Date**: |
Mon, 13 Jun 2005 11:08:21 -0500 |

Changes
http://page.axiom-developer.org/zope/mathaction/167InfiniteFloatsDomain/diff
--
How is this different than what Axiom already does?
I can write:
\begin{axiom}
a:=2*asin(1)
a::Expression Float
digits(100)
a::Expression Float
\end{axiom}
So %pi already has this kind of "closure" built-in.
Is it really possible to do this more generally for
all possible computations with real numbers?
How are "computable reals" different than actual
real numbers?
wyscc wrote:
>* Any floating point system is only, mathematically speaking,*
>* a small subset, and not evenly distributed one for that,*
>* of the reals, and for that matter, of the rationals. It is*
>* definitely not FRAC INT, which is mathematically equivalent*
>* to the field of rational numbers.*
But surely there is an isomorphism between the domain of
**infinite precision** floating point numbers and the domain
of rationals, no?
Maybe these **computable reals** are something else? Isn't
it related to the RealClosure as already implemented in
Axiom?
--
forwarded from http://page.axiom-developer.org/zope/mathaction/address@hidden

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*Bill Page* **<=**