\begin{definition}[Definition:Infimum of Set]
Let $\struct {S, \preceq}$ be an ordered set.
Let $T \subseteq S$.
An element $c \in S$ is the '''infimum of $T$ in $S$''' {{iff}}:
:$(1): \quad c$ is a lower bound of $T$ in $S$
:$(2): \quad d \preceq c$ for all lower bounds $d$ of $T$ in $S$.
If there exists an '''infimum''' of $T$ (in $S$), we say that '''$T$ admits an infimum (in $S$)'''.
\end{definition}