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\paper{sn2}{Supplement to Course Notes~6}{Asymptotic Growth
  Notation}{}
\vspace*{0.4in}
The following diagram illustrates the various kinds of asymptotic
growth relations we've covered.
\vspace*{0.1in}

\begin{figure}[h]
\begin{center}
\includegraphics[width=6in]{figures/asymp}
\end{center}
\caption{Venn Diagram describing Asymptotic Relations}
\label{asymp}
\end{figure}

For instance, if $f=o(g)$ or $f\sim g$ then it must follow that
$f=O(g)$.  However the converse is not necessarily true because there
are functions $f, g$ satisfying $f=O(g)$ which do not satisfy either
of the two prior conditions.

%Also, remember that $\Theta$ and $\sim$ describe equivalence relations over
%the set of all functions, meaning that they are 
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