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\begin{itemize}
\item What do we expect from you by way of a proof?
\item Direct proof. 
\item Proof by contradiction. $\sqrt{2}$ is irrational.
\item Proof by cases. $irrational^{irrational} = rational$ through
  $\sqrt{2}^{\sqrt{2}}$.
\item Nonconstructive proof. Infinity of primes.
\item Fallacy.
$1 = \sqrt{1} = \sqrt{(-1)(-1)} = -1$.
\end{itemize}

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