ABSTRACT
This chapter presents the frame for set theory. It proceeds at a very slow pace introducing the most basic concepts, and also the elementary conventions about mathematical notation and methods of argument and proof. A certain universe of objects is postulated and ‘collection’ appears as the only undefined term of the theory. It is expected that the reader will understand this concept and agree on some of its characteristics, notably the principle of extension for collections. Membership and inclusion are considered in this context, along with the main operations with collections.
The concept of ‘set’ is defined, as an object of the universe which is also a collection of objects of the universe. The first two axioms, empty set and pairs, are introduced, allowing the formation of ordered pairs and the definition of the cartesian product of two collections. Some properties of natural numbers, understood as auxiliary tools in reasoning but not as objects of the universe, are also part of the initial conventions.
