From 0744023a9d77661978dd956eca448828f5a38483 Mon Sep 17 00:00:00 2001
From: Joshua Potter <jrpotter2112@gmail.com>
Date: Sat, 13 May 2023 09:32:13 -0600
Subject: [PATCH] Clean-up section colors.

---
 Bookshelf/Apostol.tex  | 24 ++++++++++++------------
 Bookshelf/Enderton.tex |  6 ------
 2 files changed, 12 insertions(+), 18 deletions(-)

diff --git a/Bookshelf/Apostol.tex b/Bookshelf/Apostol.tex
index 1afecaf..349aa41 100644
--- a/Bookshelf/Apostol.tex
+++ b/Bookshelf/Apostol.tex
@@ -569,7 +569,7 @@ If there is one and only one number $c$ which satisfies the inequalities
 
 Prove that each of the following sets is measurable and has zero area:
 
-\subsection{\unverified{Exercise 1.7.1a}}%
+\subsection{\partial{Exercise 1.7.1a}}%
 \label{sub:exercise-1.7.1a}
 
 A set consisting of a single point.
@@ -585,7 +585,7 @@ A set consisting of a single point.
 
 \end{proof}
 
-\subsection{\unverified{Exercise 1.7.1b}}%
+\subsection{\partial{Exercise 1.7.1b}}%
 \label{sub:exercise-1.7.1b}
 
 A set consisting of a finite number of points in a plane.
@@ -644,7 +644,7 @@ A set consisting of a finite number of points in a plane.
 
 \end{proof}
 
-\subsection{\unverified{Exercise 1.7.1c}}%
+\subsection{\partial{Exercise 1.7.1c}}%
 \label{sub:exercise-1.7.1c}
 
 The union of a finite collection of line segments in a plane.
@@ -707,7 +707,7 @@ The union of a finite collection of line segments in a plane.
 
 \end{proof}
 
-\section{\unverified{Exercise 1.7.2}}%
+\section{\partial{Exercise 1.7.2}}%
 \label{sec:exercise-1.7.2}
 
 Every right triangular region is measurable because it can be obtained as the
@@ -758,7 +758,7 @@ Prove that every triangular region is measurable and that its area is one half
 
 \end{proof}
 
-\section{\unverified{Exercise 1.7.3}}%
+\section{\partial{Exercise 1.7.3}}%
 \label{sec:exercise-1.7.3}
 
 Prove that every trapezoid and every parallelogram is measurable and derive the
@@ -871,7 +871,7 @@ Let $P$ be a polygon whose vertices are lattice points.
 The area of $P$ is $I + \frac{1}{2}B - 1$, where $I$ denotes the number of
   lattice points inside the polygon and $B$ denotes the number on the boundary.
 
-\subsection{\unverified{Exercise 1.7.4a}}%
+\subsection{\partial{Exercise 1.7.4a}}%
 \label{sub:exercise-1.7.4a}
 
 Prove that the formula is valid for rectangles with sides parallel to the
@@ -899,7 +899,7 @@ Prove that the formula is valid for rectangles with sides parallel to the
 
 \end{proof}
 
-\subsection{\unverified{Exercise 1.7.4b}}%
+\subsection{\partial{Exercise 1.7.4b}}%
 \label{sub:exercise-1.7.4b}
 
 Prove that the formula is valid for right triangles and parallelograms.
@@ -948,7 +948,7 @@ Prove that the formula is valid for right triangles and parallelograms.
 
 \end{proof}
 
-\subsection{\unverified{Exercise 1.7.4c}}%
+\subsection{\partial{Exercise 1.7.4c}}%
 \label{sub:exercise-1.7.4c}
 
 Use induction on the number of edges to construct a proof for general polygons.
@@ -1014,7 +1014,7 @@ Use induction on the number of edges to construct a proof for general polygons.
 
 \end{proof}
 
-\section{\unverified{Exercise 1.7.5}}%
+\section{\partial{Exercise 1.7.5}}%
 \label{sec:exercise-1.7.5}
 
 Prove that a triangle whose vertices are lattice points cannot be equilateral.
@@ -1050,7 +1050,7 @@ ways, using Exercises 2 and 4.]
 
 \end{proof}
 
-\section{\unverified{Exercise 1.7.6}}%
+\section{\partial{Exercise 1.7.6}}%
 \label{sec:exercise-1.7.6}
 
 Let $A = \{1, 2, 3, 4, 5\}$, and let $\mathscr{M}$ denote the class of all
@@ -1385,7 +1385,7 @@ State and prove such a generalization.
 
 \end{proof}
 
-\section{\unverified{Exercise 1.11.6}}%
+\section{\partial{Exercise 1.11.6}}%
 \label{sec:exercise-1.11.6}
 
 Recall that a lattice point $(x, y)$ in the plane is one whose coordinates are
@@ -1438,7 +1438,7 @@ When $b = 1$, the sum on the left is understood to be $0$.
 \note{When $b = 1$, the proofs of (a) and (b) are trivial. We continue under the
   assumption $b > 1$.}
 
-\subsection{\unverified{Exercise 1.11.7a}}%
+\subsection{\partial{Exercise 1.11.7a}}%
 \label{sub:exercise-1.11.7a}
 
 Derive this result by a geometric argument, counting lattice points in a right
diff --git a/Bookshelf/Enderton.tex b/Bookshelf/Enderton.tex
index 4112570..0773151 100644
--- a/Bookshelf/Enderton.tex
+++ b/Bookshelf/Enderton.tex
@@ -27,10 +27,4 @@ Assume that $\langle x_1, \ldots, x_m \rangle =
   \langle y_1, \ldots, y_m, \ldots, y_{m+k} \rangle$.
 Then $x_1 = \langle y_1, \ldots, y_{k+1} \rangle$.
 
-\begin{proof}
-
-  TODO
-
-\end{proof}
-
 \end{document}