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# 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.

Citation Info

• [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/