Started on assignment 4

assignments/main_text.tex

@@ -17,4 +17,6 @@
 \subfile{week2/main.tex}
 \clearpage
 \subfile{week3/main.tex}
+\clearpage
+\subfile{week4/main.tex}
 \end{document}

assignments/week4/main.tex

@@ -0,0 +1,27 @@
+\documentclass[../main_text.tex]{subfiles}
+\begin{document}
+\setcounter{exercise}{0}
+
+\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}
+
+\end{document}