lower bound

Let \(X\) be an ordered set, and let \(A\) be a subset of \(X\). Then an element \(l\) of \(X\) is said to be a lower bound of \(A\) if \( l \leq a \) for every \(a\in A\). If in addition \(l \geq m \) for every lower bound \(m\) of \(A\), then \(l\) is said to be a greatest lower bound or infimum of \(A\).

The terms upper bound, least upper bound, and supremum are defined analogously.