Advanced Microeconomics/Revealed Preferences

Weak Axiom of Revealed Preferences
The demand function $$x(p,w)$$ satisfies the weak axiom of revealed preference if: $$\forall (p,w),(p^{\prime},w^{\prime}) \mbox{ if } p x(p^{\prime},w^{\prime}) \leq w \mbox{ and } x(p^{\prime},w^{\prime})\neq x({p},{w}) \mbox{ then } p^{\prime}x({p},{w}) > w^{\prime}$$

In words: The consumer faced with $$(p,w)$$ could have chosen $\funcd{x}{p^{\prime},w^{\prime}}$ but chose $$x(p,w)$$, assuming the consumer chooses consistently, if $\funcd{x}{p^{\prime},\primd{w}}$ is ever chosen, $$x(p,w)$$ must not be affordable. Hence, $$p^{\prime}\cdot x(p,w) > w^{\prime}$$