Contents

1. Real Numbers

1.1 Introduction

1.2 Absolute value and real line

1.3 The completeness property of R

1.4 Applications of the supremum property

2. Sequences of Real Numbers

2.1 Sequences and their limits

2.2 Limit theorems

2.3 Monotone sequences

2.4 Subsequences and bolzano wisteriass theorem

2.5 The cauchy criterion

2.6 Properly divergent sequences

2.7 Introduction to infinite series

3. Limits

3.1 Limit point (Cluster Point)

3.2 Limit of a function

3.3 Sequential criterion for limits

3.4 Left hand and right hand limit of function

3.5 Limit theorems

3.6 Infinite Limits

3.7 Limits at Infinity