Finished all chapters and definitions. I need to add subsections and see if there's any theorems or definitions in the appendicies that are worth adding to this as well.

chapter-1/maximal-linearly-independent-subsets.tex

@@ -7,7 +7,7 @@
 
 \begin{definition}
 	\hfill\\
-	Let $\mathcal{F}$ be the family of all subsets of a nonempty set $S$. This family $\mathcal{F}$ is called the \textbf{power set} of $S$. 
+	Let $\mathcal{F}$ be the family of all subsets of a nonempty set $S$. This family $\mathcal{F}$ is called the \textbf{power set} of $S$.
 \end{definition}
 
 \begin{definition}
@@ -18,14 +18,14 @@
 \begin{definition}[\textbf{Maximal Principle}]
 	\hfill\\
 	Let $\mathcal{F}$ be a family of sets. If, for each chain $\mathcal{C} \subseteq \mathcal{F}$, there exists a member of $\mathcal{F}$ that contains each member of $\mathcal{C}$, then $\mathcal{F}$ contains a maximal member.\\
-	
+
 	\textbf{Note:} The \textit{Maximal Principle} is logically equivalent to the \textit{Axiom of Choice}, which is an assumption in most axiomatic developments of set theory.
 \end{definition}
 
 \begin{definition}
 	\hfill\\
 	Let $S$ be a subset of a vector space $V$. A \textbf{maximal linearly independent subset} of $S$ is a subset $B$ of $S$ satisfying both of the following conditions
-	
+
 	\begin{enumerate}
 		\item $B$ is linearly independent.
 		\item The only linearly independent subset of $S$ that contains $B$ is $B$ itself.
@@ -35,4 +35,4 @@
 \begin{corollary}
 	\hfill\\
 	Every vector space has a basis.
-\end{corollary}
+\end{corollary}