ABSTRACT
This chapter begins by recalling some standard terminology and notation. Mathematics may be regarded as the study of sets and their properties. A set is a fundamental object, that cannot be defined in terms of other (simpler) objects. Intuitively, however, a set is a collection of elements. It discusses regarding some concepts relevant to Real Analysis, about infinity, extended arithmetics and suprema in the extended real line. The chapter identifies an appropriate way to compare any two sets in terms of their "size". For finite sets this is easy, since to any such set we can assign the number of elements of the set, which is a natural number. On the other hand, while it is reasonable to declare that any infinite set has more elements than any finite set, given any two infinite sets we would like to be able to say more about their relative size than merely the fact that they are both infinite.
