Question about statement of axiom of choice Here is a statement of axiom of choice given in Folland's book Real Analysis.
If $\{X_\alpha\}$ is a nonempty collection of nonempty sets, then, $\Pi  X_\alpha$ is empty.
What does it mean to say "a nonempty collection"? Isn't it just enough to say that a collection of nonempty sets? 


What does it mean to say "a nonempty collection"?

It means that the collection $\{X_\alpha\}_{\alpha \in A}$ itself is non-empty, i.e., that the indexing set $A$ is non-empty.

Isn't it just enough to say that a collection of nonempty sets?

No, because $\emptyset$ is a collection of non-empty sets.
