Understanding Infinity

PART I FROM CALCULUS TO ANALYSIS CHAPTER I.1 What's Wrong with the Calculus? CHAPTER I.2 Growth and Change in Mathematics PART II NUMBER CHAPTER II.1 Mathematics: Rational or Irrational? CHAPTER II.2 Constructive and Non-constructive Methods in Mathematics "CHAPTER II.3 Common Measures, Highest Common Factors and the Game of Euclid" CHAPTER II.4 Sides and Diagonals of Regular Polygons CHAPTER II.5 Numbers and Arithmetic?A Quick Review CHAPTER II.6 Infinite Decimals (Part 1) CHAPTER II.7 Infinite Decimals (Part 2) CHAPTER II.8 Recurring Nines CHAPTER II.9 Fractions and Recurring Decimals CHAPTER II.10 The Fundamental Property of Real Numbers CHAPTER II.11 The Arithmetic of Infinite Decimals CHAPTER II.12 Reflections on Recurring Themes CHAPTER II.13 Continued Fractions PART III GEOMETRY CHAPTER III.1 Numbers and Geometry CHAPTER III.2 The Role of Geometrical Intuition CHAPTER III.3 Comparing Areas CHAPTER III.4 Comparing Volumes CHAPTER III.5 Curves and Surfaces PART IV FUNCTIONS CHAPTER IV.1 What Is a Number? CHAPTER IV.2 What Is a Function? CHAPTER IV.3 What Is an Exponential Function? Index Errata