ABSTRACT
In this chapter I am going to introduce you to the notion of a continuous function of the real numbers. This is a topic that deserves a whole book to itself, but I am giving you this little taster here for several reasons. First, this notion is the right setting in which to prove the existence of n th roots of positive real numbers, which I promised to do way back in Chapter 5. Second, one can quite quickly develop enough theory to prove a famous result called the Intermediate Value Theorem, which sheds quite a bit of light on the great Fundamental Theorem of Algebra, stated in Chapter 7. And last, the idea of a continuous function provides yet another example of something natural and obvious-sounding being turned into rigorous mathematics, with fruitful results.
