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Lectures on the Hyperreals: An Introduction to Nonstandard Analysis (Graduate Texts in Mathematics, 188)

Lectures on the Hyperreals: An Introduction to Nonstandard Analysis (Graduate Texts in Mathematics)

Penned By Robert Goldblatt
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Lectures on the Hyperreals: An Introduction to Nonstandard Analysis (Graduate Texts in Mathematics, 188)

Lectures on the Hyperreals: An Introduction to Nonstandard Analysis (Graduate Texts in Mathematics)

Penned By Robert Goldblatt
4.85 30,427 Ratings
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Editor's Note:
This is an introduction to nonstandard analysis based on a course of lectures given several times by the author. It is suitable for use as a text at the beginning graduate or upper undergraduate level, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers but as a radically different way of viewing many standard mathematical concepts and constructions; a source of new ideas, objects and proofs; and a wellspring of powerful new principles of reasoning (transfer, overflow, saturation, enlargement, hyperfinite approximation, etc.).The book begins with the ultrapower construction of hyperreal number systems and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective, emphasizing the role of the transfer principle as a working tool of mathematical practice. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line, Ramsey's theorem, nonstandard constructions of p-adic numbers and power series, and nonstandard proofs of the Stone representation theorem for Boolean algebras and the Hahn-Banach theorem.Features of the text include an early introduction of the ideas of internal, external, and hyperfinite sets, and a set-theoretic approach to enlargements more axiomatic than the usual one based on superstructures.

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Released October 1, 1998
Identifier (ISBN) 2245546
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After spending years working in the corporate world, Robert Goldblatt finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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