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\begin{center}\textbf{Problem Set 1 \hspace{.7in} Real Analysis 1 \hspace{.7in} Due 9/4/20} \end{center}

\noindent Four of these problems will be graded, with each problem worth 5 points.  Clear and complete justification is required for full credit.  You are welcome to discuss these problems with anyone and everyone, but must write up your own final submission without reference to any sources other than the textbook and instructor. 

\begin{enumerate}
\item Prove Theorem 1.7.2(a) for the multiplicative case.

\item Prove Theorem 1.7.2(b) for the additive case.

\item Prove Theorem 1.7.2(e).

\item Prove Theorem 1.7.2(f).

\item Prove Theorem 1.7.2(g).

\item Prove Theorem 1.7.4(b).

\item Prove Theorem 1.7.4(c).

\item Prove Theorem 1.7.4(d).

\item Prove Theorem 1.7.7.

\item Prove that parts (a) and (b) of Theorem 1.7.9 are equivalent.

\item Prove Theorem 1.8.4(b).

\item Prove Theorem 1.8.5(c).

\end{enumerate}

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