# 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.

- [MLA] “lower bound.”
*Platonic Realms Interactive Mathematics Encyclopedia.*Platonic Realms, 19 Mar 2013. Web. 19 Mar 2013. <http://platonicrealms.com/> - [APA] lower bound (19 Mar 2013). Retrieved 19 Mar 2013 from the
*Platonic Realms Interactive Mathematics Encyclopedia:*http://platonicrealms.com/encyclopedia/lower-bound/