TL;DRAbstract
In this chapter we set out some of the foundations of the mathematics described in the rest of the book. We begin by examining sets and the basic operations on them. This material will, at least in part, be familiar to many readers but if you do not feel entirely comfortable with set-theoretic notation and terminology you should work through the first section carefully. The second section discusses functions: a rigorous definition of ‘function’ is included and we present various elementary properties of functions that we will need. Relations are the topic of the third section. These include functions, but also encompass the important notions of partial order and equivalence relation.
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In this chapter we set out some of the foundations of the mathematics described in the rest of the book. We begin by examining sets and the basic operations on them. This material will, at least in part, be familiar to many readers but if you do not feel entirely comfortable with set-theoretic notation and terminology you should work through the first section carefully. The second section discusses functions: a rigorous definition of ‘function’ is included and we present various elementary properties of functions that we will need. Relations are the topic of the third section. These include functions, but also encompass the important notions of partial order and equivalence relation.
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