title: "Cartesian Product"

Cartesian Product

Definition. The Cartesian product $A \times B$ of sets $A$ and $B$ is the set of all ordered pairs $(a, b)$ with $a \in A$ and $b \in B$.

It is the home of relations and functions (both are subsets of a product), and of product constructions: running two machines side by side pairs their states, which is how closure under intersection is proved in Lecture 4. Defined in Lecture 2.