ABSTRACT
This chapter studies relations and functions, which are two of the most central ideas in mathematics. It describes an arrow diagram and a graph of a relation. The chapter introduces some concepts for relations, such as inverses, composition, and identity relations, that foreshadow and generalize the corresponding concepts for functions. It states and proves many properties of inverses, identity relations, and compositions. The chapter gives a formal definition of functions within the framework of set theory. It illustrates the logical nuances of this definition with many examples of functions and non-functions. The chapter provides some basic examples of functions, such as constant functions, identity functions, inclusion functions, characteristic functions, and arithmetic functions. It introduced operations that can be used to construct new functions from old functions. The chapter investigates three operations for building new functions from given functions: composition, restriction, and gluing. It also discusses three special kinds of functions, called injections, surjections, and bijections.
