by analogy, the subset of the cartesian product "x"×"x" of any set "x" with itself, consisting of all pairs (x,x), is called the diagonal, and is the graph of the equality relation on "x" or equivalently the graph of the identity function from "x" to "x". this plays an important part in geometry; for example, the fixed points of a mapping "f" from "x" to itself may be obtained by intersecting the graph of "f" with the diagonal.