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Number Systems and the Foundations of Analysis - (Dover Books on Mathematics) (Paperback)

About this item


Number of Pages: 368

Genre: Mathematics

Sub-Genre: Number Theory

Series Title: Dover Books on Mathematics

Format: Paperback

Publisher: Dover Publications

Age Range: Adult

Author: Elliott Mendelson & Underwood Dudley & Mathematics

Language: English

TCIN: 77734814
UPC: 9780486457925
Item Number (DPCI): 247-61-3153


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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