An Introduction to Financial Mathematics, 2nd Edition

Appendix A

Basic Combinatorics

In this appendix we set out the principles of counting that are needed in the chapters on probability. As the objects to be counted are members of sets, we shall use the language and notation of sets in describing these principles. Thus we begin with a brief description of elementary set theory.

Set Theory

A set is a collection of objects called the members or elements of the set. Abstract sets are usually denoted by capital letters A, B, and so forth. If x is a member of the set A, we write x ∈ A; otherwise, we write x ∉ A. The empty set, denoted by $\cancel{0}$, is the set with no members.

A set can be described either by words, by listing the elements, or by set-builder notation. Set builder notation is of the form {x