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[Axiom-developer] [RealNumbers]

From: billpage
Subject: [Axiom-developer] [RealNumbers]
Date: Tue, 14 Jun 2005 23:36:03 -0500


Computable Numbers

  In mathematics, theoretical computer science and mathematical logic,
the computable numbers, also known as the recursive numbers, are the
subset of the real numbers consisting of the numbers which can be
computed by a finite, terminating algorithm. They can be defined
equivalently using the axioms of recursive functions, Turing machines
or lambda-calculus. In contrast, the reals require the more powerful
axioms of Zermelo-Fraenkel set theory. The computable numbers form a
real closed field and can be used in the place of real numbers for some,
but by no means all, mathematical purposes.


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