TITLE: Sets raised to exponents
QUESTION [6 upvotes]: "Find two non-empty sets $A$ and $B$ for which $A^B$ and $B^A$ are not the same size."
I'm really not sure what this means or how to even go about attempting this... Can anyone provide an example of what it means for a set to be raised to an exponent of this sort?

REPLY [5 votes]: $S^T$ is the set of all functions with domain $T$ and codomain $S$.
The reason for the notation is $$\left \vert {S^T}\right \vert = |S|^{|T|}$$