9

Injections, surjections and bijections

In defining a function *f*: *X* → *Y* we insist that a unique element of *Y* is assigned to each element of *X.* However, we do not require that each element of *Y* is assigned to some element of *X* nor do we prevent the possibility of the same element of *Y* being assigned to several (or even all the) elements of *X.* By imposing additional conditions concerning the number of elements of *X* to which elements of *Y* are assigned we get functions with particular properties. In this chapter we consider functions with particularly good properties and in particular functions which are *bijections* for which we can define an inverse function.

**Definition 9.1.1** *Suppose that f: X* → *Y is a function.*

(i) ...

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