\begin{definition}[Definition:Lower Bound of Set]
Let $\struct {S, \preceq}$ be an ordered set.
Let $T$ be a subset of $S$.
A '''lower bound for $T$ (in $S$)''' is an element $m \in S$ such that:
:$\forall t \in T: m \preceq t$
That is, $m$ precedes every element of $T$.
\end{definition}