Definition:Ordering on Mappings

Definition
Let $S$ be a set.

Let $\left({T, \preceq}\right)$ be an ordered set.

Let $f, g: S \to T$ be mappings.

Then order on mappings $f$ and $g$ denoted $f \preceq g$ is defined by
 * $\forall s \in S: f\left({s}\right) \preceq g\left({s}\right)$