# Pointwise order

The order on the set of functions with values in a partially ordered set. If $f$ and $g$ are functions from $X$ to $Y$, where $(Y,<)$ is ordered, then there is an order relation on $Y^X$ defined by $$f \le g \Leftrightarrow \forall x \in X\,,\ f(x) \le g(x) \ .$$