ABSTRACT

In this book we propose to develop a portion of mathematics from the beginning. Since the most widely accepted basis for mathematics today is the theory of sets, we shall begin our study with the notion of set. It is possible to treat set theory itself as an abstract mathematical discipline, taking set and membership as unde­ fined notions and laying down axioms to describe the interrelationships of these concepts; however, we shall not do this. We shall rely on intuition for the meaning of the ideas of set and membership and for the validity of the various set-theoretic techniques.