\begin{definition}[Definition:Ordered Set of All Mappings]
Let $L = \left({S, \preceq}\right)$ be an ordered set.
Let $X$ be a set.
The '''ordered set of all mappings''' from $X$ to $L$ is defined by:
:$L^X := \left({S^X, \precsim}\right)$
where
:$\forall f, g \in S^X: f \precsim g \iff f \preceq g$
:$\preceq$ denotes the ordering on mappings,
:$S^X$ denotes the set of all mappings from $X$ into $S$.
\end{definition}