Numbers: Rational and Irrational by Ivan Morton Niven

Numbers: Rational and Irrational



Download Numbers: Rational and Irrational




Numbers: Rational and Irrational Ivan Morton Niven
Language: English
Page: 145
Format: djvu
ISBN: 0883856018, 9780883856017
Publisher: Mathematical Association of America

Series: Anneli Lax New Mathematical Library

A superb development that starts with the natural numbers and carries the reader through the rationals and their decimal representations to algebraic numbers and then to the real numbers. Along the way, you will see characterizations of the rationals and of certain special (Liouville) transcendental numbers. This material is basic to all of algebra and analysis.

This book deals with the number system, one of the basic structures in mathematics. It is concerned especially with ways of classifying numbers into various categories; for example, it provides some criteria for deciding if a given number is rational (i.e., representable as a common fraction) or irrational, if it is algebraic or transcendental. In the course of the later chapters, the reader is introduced to some of the more recent developments in mathematics. Professor Niven’s book may be read with profit by interested high school students as well as by college students and others who want to know more about the basic aspects of pure mathematics. Most readers will find the early chapters well within their grasp while ambitious readers will profit by the more advanced material to be found in later chapters.

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