Cartesian Products

Cartesian products are named after the French philosopher and mathematician Rene Descartes. They can be defined as follows:

A X B = {(a,b): where a is an element in A and b is an element in B}

Consider the example:

A={1,2} and B={2,3,4}

then the Cartesian product of A and B is written as follows:

A X B = {(1,2),(1,3),(1,4),(2,2),(2,3),(2,4)}

Order does matter in Cartesian products, contrast the following:

B X A = {(2,1),(2,2),(3,1),(3,2),(4,1),(4,2)}