In real numbers, the cube function preserves the order: larger numbers have larger cubes. In other words, cubes (strictly) monotonically increase. Also, its codomain is the entire real line: the function is a surjection (takes all possible values). Only three numbers are equal to their own cubes: , , and . If or , then . If or , then . All aforementioned properties pertain also to any higher odd power (, , ...) of real numbers. Equalities and inequalities are also true in any ordered ring.