upper bound

Let $S$ be a set with a partial ordering $\le$, and let $T$ be a subset of $S$. An upper bound for $T$ is an element $z\in S$ such that $x\le z$ 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