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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
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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?
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