Suppose $\displaystyle (A,\leq)$ is a well-ordered set. Let $\displaystyle B = \mathbb{R}^A$. Find an explicit linear order on $\displaystyle B$.

So I have to prove reflexivity, antisymmetry, transitivity and that B is linear. Thing is I cant really get my head around what $\displaystyle B = \mathbb{R}^A$ actually is... Set of functions from A to $\displaystyle \mathbb{R}$. But A is well ordered... So how does that change things?

Does this involve creating an in/bijection between B and some well ordered set?