\problemdata      
        {?} % latex-friendly label for the prob.
        {Infinite Sets} % The topic(s) of the problem content.
        {?} % Source (if known)
        {Fall 2001, final} % Usage (list ones you are aware of).
        {Christos Kapoutsis, S02} % Last revision info (author, date).


\begin{problem}
Describe two infinite sets $A$ and $B$ such that there
no surjection from $A$ to $B$.  Indicate whether conversely there is a 
surjection from $B$ to $A$.  No proofs are required.

\solution{
No surjection from $A$ to $B$ is equivalent to no injection
from $B$ to $A$, so $(A,B)$ for example could be $(\naturals, \reals)$ or
$(I,\power(I))$ for any infinite set $I$.  There will always be a
surjection in the other direction.
}
\end{problem}