**8**

Functions

The notion of *function* is one of the most fundamental in mathematics. It is probably familiar to the reader in the context of calculus, and it is here that the concept was first clarified and the difference between a function and a formula properly understood in the early years of the nineteenth century. Today, the language of functions is used throughout mathematics.

In this chapter the function concept is introduced. We discuss various ways of defining a function and consider the graph of a function.

**Definition 8.1.1** *Suppose that X and Y are sets. A *, map *or* mapping *from the set X to the set Y is the ...*

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