Symmetric edits

Advanced/Symmetric Group/main.tex

@@ -35,14 +35,14 @@
 	\section{Bonus problems}
 
 	\problem{}
-	Show that $x$ has a multiplicative inverse mod $n$ iff $\text{gcd}(x, n) = 1$
+	Show that $x \in \mathbb{Z}^+$ has a multiplicative inverse mod $n$ iff $\text{gcd}(x, n) = 1$
 
 	\vfill
 
 	\problem{}
 	Let $\sigma = (\sigma_1 \sigma_2 ... \sigma_k)$ be a $k$-cycle in $S_n$, and let $\tau$ be an arbitrary element of $S_n$. \par
 	Show that $\tau \sigma \tau^{-1}$ = $\bigl(\tau(\sigma_1), \tau(\sigma_2), ..., \tau(\sigma_k)\bigr)$ \par
-	\hint{As usual, $\sigma$ is a permutation. Thus, $\sigma(x)$ is the value at position $x$ after applying $\sigma$.}
+	\hint{As usual, $\tau$ is a permutation. Thus, $\tau(x)$ is the value at position $x$ after applying $\tau$.}
 
 	\vfill