For the two Prefaces see Landau's Foundations.
## FOUNDATIONS OF ANALYSIS## THE ARITHMETIC OF |

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

JOC/EFR August 2007

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