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\lhead{MATH 311-01}
\chead{Problem of the Day}
\rhead{YOUR NAME HERE}
\lfoot{}
\cfoot{Page \thepage\ of \pageref{LastPage}}
\rfoot{\textbf{due October 2, 2013}}
\begin{document}
\begin{enumerate}
\item Prove that there is no largest number in the open interval $(3,6)$.

  \begin{proof}
    
  \end{proof}

\item Demonstrate that the above result is not true of the closed
  interval $[3,6]$. What aspect of your proof would not work in this
  case?


  % Answer here!

\item Prove that, for an irrational number $\alpha$ and a nonzero
  rational number $x$, their product $\alpha x$ is irrational.

  \begin{proof}
    
  \end{proof}
\end{enumerate}
\end{document}
