Titlebook: A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton’s Prin; Jacques Fleuriot Book 2001 Springer-

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Basic Concepts and Preliminaries,ow describe the use of the hyperreals as valuable tools for mathematical analysis. Through the existence of infinitesimals, finite, and infinite numbers, NSA provides us with a rich structure which we use to formalize alternative treatments of topics in classical analysis. Such treatments are not on

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Basic structure and metabolism of isomalt, NSA. The idea was to introduce a new number system known as the . which contains the real numbers but also infinitesimals and infinite numbers. The notions of infinitesimals and other nonstandard numbers introduce many subtleties into the theory that need to be dealt with.

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978-1-4471-1041-5Springer-Verlag London 2001

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Book 2001ocedures, which respects much of Newton‘s original reasoning, is developed within the theorem prover Isabelle. The application of this framework to the mechanization of elementary real analysis using nonstandard techniques is also discussed.

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of the procedures, which respects much of Newton‘s original reasoning, is developed within the theorem prover Isabelle. The application of this framework to the mechanization of elementary real analysis using nonstandard techniques is also discussed.978-1-4471-1041-5978-0-85729-329-9

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Basic structure and metabolism of isomalt,omain emerged and no significant results could be proved. The developments over the last twenty years or so though have led to a revolution in the field. We survey several of the powerful methods proposed and analyse our own choice for formalization in Isabelle. Concepts that are important to deal with the geometry of the . are also introduced.