UpperBound 2001-10-21 02:37:39 2004-03-20 23:32:06 Definition bound lower bound bounded bounded from above bounded from below \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} Let $S$ be a set with a partial ordering $\leq$, and let $T$ be a subset of $S$. An {\em upper bound} for $T$ is an element $z \in S$ such that $x \leq z$ for all $x \in T$. We say that $T$ is {\em bounded from above} if there exists an upper bound for $T$. {\em Lower bound}, and \emph{bounded from below} are defined in a similar manner.