diff --git a/year4/semester2/CT421/notes/CT421.pdf b/year4/semester2/CT421/notes/CT421.pdf
index b2dab480..3f41628a 100644
Binary files a/year4/semester2/CT421/notes/CT421.pdf and b/year4/semester2/CT421/notes/CT421.pdf differ
diff --git a/year4/semester2/CT421/notes/CT421.tex b/year4/semester2/CT421/notes/CT421.tex
index ac7eadbf..b70ffa7d 100644
--- a/year4/semester2/CT421/notes/CT421.tex
+++ b/year4/semester2/CT421/notes/CT421.tex
@@ -155,22 +155,22 @@ The problem statement can be formalised as follows:
 
 More formally:
 \begin{itemize}
-    \item   Set of states $S$.
-    \item   Start state $s_0 \in S$.
-    \item   Set of actions $A$ and action rules $a(s) \rightarrow s'$.
-    \item   A goal test $g(s) \rightarrow \{0,1\}$.
-    \item   Cost function $C(s,a,s') \rightarrow \mathbb{R}$.
+    \item   There is a set of (possible/legal) states $S$;
+    \item   There is some start state $s_0 \in S$;
+    \item   There is a set of actions $A$ and action rules $a(s) \rightarrow s'$;
+    \item   There is some goal test $g(s) \rightarrow \{0,1\}$ that tests if we have satisfied our goal;
+    \item   There is some cost function $C(s,a,s') \rightarrow \mathbb{R}$ that associates a cost with each action;
     \item   Search can be defined by the 5-tuple $(S,s,a,g,C)$.
 \end{itemize}
 
 We can then state the problem as follows:
-find a sequence of actions $a_1 \dots a_n$ and corresponding states $s_0 \dots sn$ such that:
+find a sequence of actions $a_1 \dots a_n$ and corresponding states $s_0 \dots s_n$ such that:
 \begin{itemize}
     \item   $s_0 = s$
     \item   $s_i = a_i(S_{i-1})$
     \item   $g(s_n) = 1$
 \end{itemize}
-while minimising $\sum^n_{i=1} c(a_i)$.
+while minimising the overall cost $\sum^n_{i=1} c(a_i)$.
 \\\\
 The problem of solving a sudoku puzzle can be re-stated as:
 \begin{itemize}