ENGLISH

The Number System

By H. A. Thurston

Book information

Publisher
Dover Publications
Year
1956
ISBN
978-0486458069
ASIN
B00GUBO9HS
Language
english
Format
EPUB
Filesize
7 MB (7458794 bytes)
Series
Dover Books on Mathematics
Edition
1
Pages
144\0
Orientation
no
Paginated
yes
Scanned
yes
Time added
2015-04-22 03:57:09

Description

The teaching of mathematics has undergone extensive changes in approach, with a shift in emphasis from rote memorization to acquiring an understanding of the logical foundations and methodology of problem solving. This book offers guidance in that direction, exploring arithmetic's underlying concepts and their logical development. This volume's great merit lies in its wealth of explanatory material, designed to promote an informal and intuitive understanding of the rigorous logical approach to the number system. The first part explains and comments on axioms and definitions, making their subsequent treatment more coherent. The second part presents a detailed, systematic construction of the number systems of rational, real, and complex numbers. It covers whole numbers, hemigroups and groups, integers, ordered fields, the order relation for rationals, exponentiation, and real and complex numbers. Every step is justified by a reference to the appropriate theorem or lemma. Exercises following each chapter in Part II help readers test their progress and provide practice in using the relevant concepts. Reprint of the 1967 Dover edition.

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