Elements of Set Theory
This chapter contains a review of some essential concepts and results of set theory on which lean the following chapters. Section 1 deals mainly with operations on sets. In Section 2 we define several types of functions, and discuss the notion of a Cartesian product. In Section 3 we study the concepts of equivalent relation and partial ordering. A special attention is paid to the classification of sets according to the number of their elements. At the end of this section we state some equivalent forms of the axiom of choice.
The treatment of the set-theoretic notions is not axiomatic, but relies on intuition and elementary logic. However, this will not introduce sets which lead to paradoxes.