2.4. The Real Number System
Definition: Lower and Greatest Lower Bound
Let A be an ordered set, and X a subset of A. An element b in A is called a greatest lower bound (or infimum) for X if b is a lower bound for X and there is no other lower bound b' for X that is greater than b. We write b = inf(X).
By its definition, if a greatest lower bound exists, it is unique.