= Pointwise order
{title2=$f\preceq g\iff\forall x,\ f(x)\preceq g(x)$}
Given a <partially ordered set> $B$ and a <set> $A$, the pointwise order on the <function space> of <functions> $A\to B$ compares their values at every argument. It is a <partial order>: <reflexivity> and <transitivity> hold at every argument, and <antisymmetry> follows because two <functions> equal at every argument are equal. Even if $B$ has a <total order>, this <function space> need not: the two <functions> on $\{0,1\}$ with values $(0,1)$ and $(1,0)$ are incomparable when $B=\mathbb R$.
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