Product sets
If X and Y are sets, then X ´ Y is a new set called a product set. It is defined by:
X ´ Y = {(x,y) | x ∈ X, y ∈ Y }
That is, X ´ Y is the set of tuples formed from elements of X and elements of Y. Pictorial examples:
On the left, X is a vertical span, and Y is a horizontal span. The product set is the collection of points in the rectangular region formed by these two spans.
On the right, X is a vertical span, and Y is a set of discrete points arranged horizontally. The product set is the collection of points in the vertical lines.