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/