Introduction

This chapter is a background material on basic concepts in set theory and basic properties of real numbers.

We look at

• Basic properties of sets
• Concept of a function
• Cartesian products
• Relations
• Notion of order in sets
• Countable and uncountable sets

Concepts are developed sequentially where one concept builds upon other concepts previously defined. Examples are added wherever suitable for better understanding. In examples we use sets of real numbers, natural numbers, integers frequently. Some of their properties may not have been defined before they are used in examples. This has been done keeping in mind that the reader has an intuitive understanding of these numbers and the examples are easier to visualize.

The presentation in this chapter largely follows [AB98].