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Computing with Reals

rigour in mathematics

history of reals

logical development

formalisation

problems

Background
The Real Numbers are required for the development of the branch of Mathematics called analysis, which contains a major part of the mathematics used in science and engineering. The reals are convenient for the rigorous development of the relevant mathematial theories, but tricky when it comes to doing practical computations. Consequently, when analysis is applied the necessary computations are fudged, the answers are approximate and reliable error bounds are rarely known.
Motivation

History

Representation

Implementation

Scope and Contents
We are here concerned with understanding the problem of exact computation with real numbers well enough to support the design and implementation of tools capable of doing mathematics with formal rigour and precision and with high levels of automation and reasonable levels of computational efficiency.

It is my present belief that this can be achieved in the context classical analysis, without the need to fall back to constructive analysis. Eventually, you will be able to discover how that can be done from these pages.

Real People

A link: Papers by Pietro Di Gianantonio on Real Number Computability.
A nother:Computability and Complexity in Analysis.


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