Cartesian Products

We have a definition for the cartesian product of two sets, but we can extend this definition.

Definition

Let \mathcal{A} be a nonempty collection of sets.

An indexing function on \mathcal{A} is a surjective function f from some set J, called the index set, to \mathcal{A}.

The collection \mathcal{A} with the indexing function f is called an [indexed family of sets]