Let S be a nonempty set of real numbers that has an upper bound. Then a number c is called the least upper bound (or the supremum, denoted sup S) for S iff it satisfies the following properties: 1.c>=x for all x element S. 2. For all real numbers k, if k is an upper bound for S, then k>=c.

greatest lower bound | limit | supremum | supremum limit | upper bound