It is necessary to understand the concept of sets to express anything, be it mathematics or the behaviour of computer systems, formally. Furthermore, the notation of sets provides a concise way to express statements about computers. Much of the material in this chapter is probably familiar, but it is important to begin thoroughly, and sets are also a useful topic with which to study the writing of mathematical proofs, something which will shadow\r\nthe discrete mathematics material throughout this course. Although the idea of a set as a collection of objects (in which neither order nor duplication are significant) is simple enough, it is rather complicated to give a formal definition from scratch. We will leave the complexities to mathematical philosophers and adopt a simple working definition, but you should know that the subject called axiomatic set theory is deep and difficult.