ABSTRACT
The central concept of this chapter is that of ‘relation’, a term which is defined for classes: a relation is a class whose elements are ordered pairs. Operations with relations are defined, as well as other notions like domains or restrictions; and the idea of an order relation is then presented, along with several examples and basic properties and notions related to this type of relations, as bounds or maxima and minima. The concept of equivalence relations is also dealt with at the end of the chapter, though this is subordinate to that of partition of a class, which has a more intuitive appeal.
The second part of the chapter is focused on the functional relations, a crucial notion that will allow to include, later in the course, the fundamental classical concept of ‘function’ inside set theory. As with general relations, these functionals are defined for classes. And the basic developments about composition and injectivity of functionals, as the key for getting inverse functionals, are also treated in this part.
