pOne of the most pressingbbproblems of mathematics over the last hundred years has been the question What is a number One of the most impressive answers has been the axiomatic development of set theory. The question raised is Exactly what assumptions, beyond those of elementary logic, are required as a basis for modern mathematics Answering this question by means of the Zermelo-Fraenkel system, Professor Suppes' coverage is the best treatment of axiomatic set theory for the mathematics student on the upper undergraduate or graduate level. brThe opening chapter covers the basic paradoxes and the history of set theory and provides a motivation for the study. The second and third chapters cover the basic definitions and axioms and the theory of relations and functions. Beginning with the fourth chapter, equipollence, finite sets and cardinal numbers are dealt with. Chapter five continues the development with finite ordinals and denumerable sets. Chapter six, on rational numbers and real n