2.4. The Real Number System
Definition 2.4.2: Upper and Least Upper Bound
Let A be an ordered set, and X a subset of A. An element b in A is called a least upper bound (or supremum) for X if b is an upper bound for X and there is no other upper bound b' for X that is less than b. We write b = sup(X).
By its definition, if a least upper bound exists, it is unique.