Sets, Relations and Functions

Abstract

This chapter provides an introduction to fundamental building blocks in mathematics such as sets, relations and functions. Sets are collections of well-defined objects; relations indicate relationships between members of two sets A and B; and functions are a special type of relation where there is exactly (or at most) one relationship for each element a ∈A with an element in B. A set is a collection of well-defined objects that contains no duplicates. A binary relationbinary relationR (A, B) where A and B are sets is a subset of the Cartesian product (A × B) of A and B. The notation aRb signifies that there is a relation between a and b and that (a, b) ∈R. A total function f: A → B is a special relation such that for each element a ∈ A there is exactly one element b ∈ B. This is written as f(a) = b. A partial function differs from a total function in that the function may be undefined for one or more values of A.