# upper bound

Let $S$ be a set with a partial ordering $\leq$, and let $T$ be a subset of $S$. An for $T$ is an element $z\in S$ such that $x\leq z$ for all $x\in T$. We say that $T$ is bounded from above if there exists an upper bound for $T$.

Lower bound, and bounded from below are defined in a similar manner.

 Title upper bound Canonical name UpperBound Date of creation 2013-03-22 11:52:15 Last modified on 2013-03-22 11:52:15 Owner djao (24) Last modified by djao (24) Numerical id 9 Author djao (24) Entry type Definition Classification msc 06A06 Classification msc 11A07 Defines bound Defines lower bound Defines bounded Defines bounded from above Defines bounded from below