In 1930 Edmund Landau's
### THE ARITHMETIC OF

BY

Translated by

Columbia University

*Grundlagen der Analysis*was published by the Akademische Verlagsgesellschaft M.B.H., Leipzig. In 1951 an English translation of Landau's work by F Steinhardt of Columbia University in New York was published by the Chelsea Publishing Company. The full title, including subtitles, was*Foundations of Analysis: the Arithmetic of Whole, Rational, Irrational and Complex Number: A Supplement to Text-Books on the Differential and Integral Calculus.*Below is a list of the Contents of this interesting book.For the two Prefaces see Landau's Foundations.

## FOUNDATIONS OF ANALYSIS

### THE ARITHMETIC OF

WHOLE, RATIONAL, IRRATIONAL AND COMPLEX NUMBERS

*A Supplement to Text-Books on the*

*Differential and Integral Calculus*

### EDMUND LANDAU

**F Steinhardt**

Columbia University

**CHELSEA PUBLISHING COMPANY**

**1951**

TABLE OF CONTENTS

Preface for the Student

Preface for the Scholar

**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