The Number System
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The Number System
Author: H. A. Thurston
language: en
Publisher: Courier Corporation
Release Date: 2012-10-23
This book explores arithmetic's underlying concepts and their logical development, in addition to a detailed, systematic construction of the number systems of rational, real, and complex numbers. 1956 edition.
The Real Number System
Author: John M. H. Olmsted
language: en
Publisher: Courier Dover Publications
Release Date: 2018-09-12
Concise but thorough and systematic, this categorical discussion of the real number system presents a series of step-by-step axioms, each illustrated by examples. The highly accessible text is suitable for readers at varying levels of knowledge and experience: advanced high school students and college undergraduates as well as prospective high school and college instructors. The abundance of examples and the wealth of exercises—more than 300, all with answers provided—make this a particularly valuable book for self-study. The first two chapters examine fields and ordered fields, followed by an introduction to natural numbers and mathematical induction. Subsequent chapters explore composite and prime numbers, integers and rational numbers, congruences and finite fields, and polynomials and rational functions. Additional topics include intervals and absolute value, the axiom of completeness, roots and rational exponents, exponents and logarithms, and decimal expansions. A helpful Appendix concludes the text.
Number Systems and the Foundations of Analysis
Author: Elliott Mendelson
language: en
Publisher: Dover Books on Mathematics
Release Date: 2008
Geared toward undergraduate and beginning graduate students, this study explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Numerous exercises and appendixes supplement the text. 1973 edition.