Union and intersection are one way of generating new sets from old. Another way of generating new sets is by welding together sets of disparate objects into another set called their product. The product of two sets X and Y is the set of ordered pairs
X × Y = {(x, y): x ˆˆ X, y ˆˆ Y}
A familiar example is the coordinate plane R × R which is denoted R2 (figure 1.2). This correspondence between points in the plane and ordered pairs x; y of real numbers is the foundation of analytic geometry. Notice how the order matters. (1, 2) and (2, 1) are different elements of R2.

1,2) (2,1)