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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.

Citation Info

• [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/