Much of mathematics and its applications is concerned with the study of func-tions of various kinds. In this chapter we give the definition and some elemen-tary examples, and introduce certain important general types of functions. DEFINITION Let S and T be sets. A function from S to T is a rule
that assigns to each s ∈ S a single element of T , denoted by f (s). We write f : S→ T to mean that f is a function from S to T . If f (s) = t, we often say f sends s→ t.