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Number Systems and the Foundations of Analysis by Elliott Mendelson

Number Systems and the Foundations of Analysis

by Elliott Mendelson
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Book cover type: Paperback
  • ISBN13: 9780486457925
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Dover Publications
  • Publisher Imprint: Dover Publications
  • Publication Date:
  • Pages: 368
  • Original Price: USD 19.95
  • Language: English
  • Edition: N/A
  • Item Weight: 363 grams
  • BISAC Subject(s): Number Theory and Mathematical Analysis

This study of basic number systems explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Written by a noted expert on logic and set theory, it assumes no background in abstract mathematical thought. Undergraduates and beginning graduate students will find this treatment an ideal introduction to number systems, particularly in terms of its detailed proofs.
Starting with the basic facts and notions of logic and set theory, the text offers an axiomatic presentation of the simplest structure, the system of natural numbers. It proceeds, by set-theoretic methods, to an examination of integers that covers rings and integral domains, ordered integral domains, and natural numbers and integers of an integral domain. A look at rational numbers and ordered fields follows, along with a survey of the real number system that includes considerations of least upper bounds and greatest lower bounds, convergent and Cauchy sequences, and elementary topology. Numerous exercises and several helpful appendixes supplement the text.

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