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\part{Assignment 4}

\exercise*
\begin{tcolorbox}
    We say a set $F \subset \R$ is \textit{closed} if its complement $F^c := \R \backslash F$ is open. Since
    $\emptyset$ and $\R$ are open, it follows that $\emptyset$ and $\R$ are closed as well.

    \begin{enumerate}[label=\emph{(\alph*)}]
        \item Let $a,b \in \R$ with $a < b$. Prove that $[a,b]$ is closed.
        \item Is the set $\Z \subset \R$ closed? Provide a proof to substantiate your claim.
        \item Is the set of rationals $\Q \subset \R$ closed? Provide a proof to substantiate your claim.
    \end{enumerate}
\end{tcolorbox}

\begin{enumerate}[label=\emph{(\alph*)}
    \item The complement of $[a,b]$ is equal to the union of $(-\infty, a)$ and $(b, \infty)$. So, we have to prove
        that both these sets are open. But we have already done so in the assignment of the previous week, so I'll just
        leave it at that.
    \item 
    \item
\end{enumerate}

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