Functions

In the previous chapter, we studied a way to relate elements of one set to another set. However, we didn’t place any restrictions on those relations. Usually, we want to have some specific type of structure in the way we relate elements.

Throughout our normal schooling, we encounter many types of these structured relations. Specifically, the kinds of relations we studied were functions. In this chapter, we delve deeper into these special kind of relations, and study them in an abstract sense. That is to say, what we discuss here will be applicable to all functions, not just those more familiar functions that relate real numbers to other real numbers.