upper bound

Let \(X\) be an ordered set, and let \(A\) be a subset of \(X\). Then an element \(u\) of \(X\) is said to be an upper bound of \(A\) if \( u \geq a \) for every \(a\in A\). If in addition \(u \leq v \) for every upper bound \(v\) of \(A\), then \(u\) is said to be a least upper bound or supremum of \(A\).

The terms lower bound, greatest lower bound, and infimum are defined analogously.