Number Systems and the Foundations of Analysis

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9780124908505: Number Systems and the Foundations of 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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Written by a noted expert on logic and set theory, this study of basic number systems explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Geared toward undergraduate and beginning graduate students, it requires minimal mathematical training. Numerous exercises and several helpful appendixes supplement the text. 1973 edition.

"About this title" may belong to another edition of this title.

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Mendelson, Elliott
Published by Academic Press Inc (1973)
ISBN 10: 0124908500 ISBN 13: 9780124908505
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Published by Academic Press Inc (1973)
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Published by Academic Press Inc (1973)
ISBN 10: 0124908500 ISBN 13: 9780124908505
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