In this chapter we will discuss the essential properties of the real number system R. Although it is possible to give a formal sonctruction of this system on the basis of a more primitive set (such as the set N of natural numbers or the set Q of rational numbers), we have chosen not to do so. Instead, we exhibit a list of fundamental properties associated with the real numbers and show how further properties can be deduced from them. This kind of activity is much more useful in learning the tools of analysis than examining the logical difficultis of contructing a model for R
