# 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.

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