User:Blackbombchu/Sandbox/Definition:Distance function

A distance function is a function f from R2 to R satisfying the following conditions:
 * For all nonnegative real numbers r, f(r, 0) = r
 * For all real numbers r and s, f(r, s) is a nonnegative real number
 * For all real numbers r and s, f(r, -s) = f(r, s)
 * For all real numbers r, s, t, u, f(ru - st, rt + su) = f(r, s) × f(t, u)