Let S be a set and A a non-empty subset of S. A choice function f is defined as $\displaystyle f: A \to S$ such that $\displaystyle f(A) \in A$.

The last part is what is causing the problem. Does this mean that $\displaystyle f(A) \in A$ implies that f(A) is a single element of the subset A? If so I can work with this, but what little experience I have says f(A) should be a subset (not a single element) of S so I'm a little confused.

Thank you.

-Dan