Softcover ISBN:  9781470470579 
Product Code:  CHEL/79.S 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470470616 
Product Code:  CHEL/79.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Softcover ISBN:  9781470470579 
eBook: ISBN:  9781470470616 
Product Code:  CHEL/79.S.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 
Softcover ISBN:  9781470470579 
Product Code:  CHEL/79.S 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470470616 
Product Code:  CHEL/79.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Softcover ISBN:  9781470470579 
eBook ISBN:  9781470470616 
Product Code:  CHEL/79.S.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 

Book DetailsAMS Chelsea PublishingVolume: 79; 1966; 136 ppMSC: Primary 26; 01
Why does \(2 \times 2 = 4\)? What are fractions? Imaginary numbers? Why do the laws of algebra hold? And how do we prove these laws? What are the properties of the numbers on which the Differential and Integral Calculus is based? In other words, What are numbers? And why do they have the properties we attribute to them? Thanks to the genius of Dedekind, Cantor, Peano, Frege and Russell, such questions can now be given a satisfactory answer. This English translation of Landau's famous Grundlagen der Analysis–also available from the AMS–answers these important questions.

Table of Contents

PREFACE FOR THE STUDENT

PREFACE FOR THE TEACHER

TABLE OF CONTENTS

CHAPTER I: NATURAL NUMBERS

§1 Axioms

§2 Addition

§3 Ordering

§4 Multiplication

CHAPTER II: FRACTIONS

§1 Definition and Equivalence

§2 Ordering

§3 Addition

§4 Multiplication

§5 Rational Numbers and Integers

CHAPTER III: CUTS

§1 Definition

§2 Ordering

§3 Addition

§4 Multiplication

§5 Rational Cuts and Integral Cuts

CHAPTER IV: REAL NUMBERS

§1 Definition

§2 Ordering

§3 Addition

§4 Multiplication

§5 Dedekind's Fundamental Theorem

CHAPTER V: COMPLEX NUMBERS

§1 Definition

§2 Addition

§3 Multiplication

§4 Subtraction

§5 Division

§6 Complex Conjugates

§7 Absolute Value

§8 Sums and Products

§9 Powers

§10 Incorporation of the Real Numbers into the System of Complex Numbers

INDEX

Blank Page


Additional Material

Reviews

Certainly no clearer treatment of the foundations of the number system can be offered ... one can only be thankful to the author for this fundamental piece of exposition, which is alive with his vitality and genius.
American Mathematical Monthly


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Why does \(2 \times 2 = 4\)? What are fractions? Imaginary numbers? Why do the laws of algebra hold? And how do we prove these laws? What are the properties of the numbers on which the Differential and Integral Calculus is based? In other words, What are numbers? And why do they have the properties we attribute to them? Thanks to the genius of Dedekind, Cantor, Peano, Frege and Russell, such questions can now be given a satisfactory answer. This English translation of Landau's famous Grundlagen der Analysis–also available from the AMS–answers these important questions.

PREFACE FOR THE STUDENT

PREFACE FOR THE TEACHER

TABLE OF CONTENTS

CHAPTER I: NATURAL NUMBERS

§1 Axioms

§2 Addition

§3 Ordering

§4 Multiplication

CHAPTER II: FRACTIONS

§1 Definition and Equivalence

§2 Ordering

§3 Addition

§4 Multiplication

§5 Rational Numbers and Integers

CHAPTER III: CUTS

§1 Definition

§2 Ordering

§3 Addition

§4 Multiplication

§5 Rational Cuts and Integral Cuts

CHAPTER IV: REAL NUMBERS

§1 Definition

§2 Ordering

§3 Addition

§4 Multiplication

§5 Dedekind's Fundamental Theorem

CHAPTER V: COMPLEX NUMBERS

§1 Definition

§2 Addition

§3 Multiplication

§4 Subtraction

§5 Division

§6 Complex Conjugates

§7 Absolute Value

§8 Sums and Products

§9 Powers

§10 Incorporation of the Real Numbers into the System of Complex Numbers

INDEX

Blank Page

Certainly no clearer treatment of the foundations of the number system can be offered ... one can only be thankful to the author for this fundamental piece of exposition, which is alive with his vitality and genius.
American Mathematical Monthly