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Number Systems: Constructions and Properties

by Rana Inder K

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Building the number systems from set theory

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Hardcover New English

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AlbakiReads Editorial

Building the number systems from set theory

Beginning with Zermelo–Fraenkel axiomatic set theory, Rana Inder K develops the real and complex numbers step by step, then establishes their basic properties, including a proof of the Fundamental Theorem of Algebra. Historical notes trace how number systems evolved, while brief sketches introduce some of the mathematicians involved. The construction-oriented approach supplies a logical foundation for analysis and a starting point for abstract algebra, complementing real-analysis texts that take the real numbers as given. The book is organized for use in a post-calculus foundations course or seminar, and is also presented as a resource for independent study.

Good fit for readers who enjoy

  • Post-calculus students studying the foundations of analysis
  • School and college teachers seeking material for self-study
  • Readers interested in the construction and historical development of number systems

Themes

Axiomatic set theoryConstruction of real and complex numbersFoundations of analysisHistory of mathematics

Based on publisher information and book metadata.

Book overview

Starting with the Zermelo-Fraenhel axiomatic set theory, this book gives a self-contained, step-by-step construction of real and complex numbers. The basic properties of real and complex numbers are developed, including a proof of the Fundamental Theorem of Algebra. Historical notes outline the evolution of the number systems and alert readers to the fact that polished mathematical concepts, as presented in lectures and books, are the culmination of the efforts of great minds over the years. The text also includes short life sketches of some of the contributing mathematicians. The book provides the logical foundation of Analysis and gives a basis to Abstract Algebra. It complements those books on real analysis which begin with axiomatic definitions of real numbers.The book can be used in various ways: as a textbook for a one semester course on the foundations of analysis for post-calculus students; for a seminar course; or self-study by school and college teachers.

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