The How and Why of One Variable Calculus

Preface ix

Introduction xi

Preliminary notation xv

1 The real numbers 1

1.1 Intuitive picture of R as points on the number line 2

1.2 The field axioms 6

1.3 Order axioms 8

1.4 The Least Upper Bound Property of R 9

1.5 Rational powers of real numbers 20

1.6 Intervals 21

1.7 Absolute value |·|and distance in R 23

1.8 (∗) Remark on the construction of R 26

1.9 Functions 28

1.10 (∗) Cardinality 40

Not...