Applied edits

Advanced/Linear Algebra 101/parts/0 notation.tex

@@ -7,7 +7,7 @@
 	\item $\mathbb{R}^+_0$ is the set of positive real numbers and zero.
 \end{itemize}
 
-Mathematicians are often inconsistent with their notation. Depending on the author, their mood, and the phase of the moon, $\mathbb{R}^+$ may or may not include zero. I will use the definitions above.
+Mathematicians are often inconsistent with their notation. Depending on the author, their mood, and the phase of the moon, $\mathbb{R}^+$ may or may not include zero. We will use the definitions above.
 
 
 \definition{}
@@ -64,12 +64,12 @@ What is $\mathbb{R} \times \mathbb{R}$? \\
 
 \definition{}
 $\mathbb{R}^n$ is the set of $n$-tuples of real numbers. \\
-In english, this means that an element of $\mathbb{R}^n$ is a list of $n$ real numbers: \\
+In English, this means that an element of $\mathbb{R}^n$ is a list of $n$ real numbers: \\
 
 \vspace{4mm}
 
 Elements of $\mathbb{R}^2$ look like $(a, b)$, where $a, b \in \mathbb{R}$. \hfill \note{\textit{Note:} $\mathbb{R}^2$ is pronounced \say{arrgh-two.}}
-Elements of $\mathbb{R}^5$ look like $(a_1, a_2, a_3, a_4 a_5)$, where $a_n \in \mathbb{R}$. \\
+Elements of $\mathbb{R}^5$ look like $(a_1, a_2, a_3, a_4, a_5)$, where $a_n \in \mathbb{R}$. \\
 
 $\mathbb{R}^1$ and $\mathbb{R}$ are identical.