diff --git a/math/proof/notes.page b/math/proof/notes.page
index 5167c35..efd3ca3 100644
--- a/math/proof/notes.page
+++ b/math/proof/notes.page
@@ -139,7 +139,7 @@ A,i \in \{1,\dots,n\}\} $$
 **Definition 1.3**
 : $A$ and $B$ are sets. If every element of $A$ is also an element of
 $B$, then $A$ is a *subset* of $B$ and we write $A \subseteq B$. If
-this is not the case, we write $A \subsetneq B$, which means there is
+this is not the case, we write $A \not\subseteq B$, which means there is
 at least one element of $A$ that is not in $B$.
 
 **Fact 1.2**
@@ -161,7 +161,7 @@ $2^n$ total leaves of the tree.
 
 1. Subsets of \{1,2,3,4\}: $\emptyset, \{1\}, \{2\}, \{3\}, \{4\},
    \{1,2\}, \{1,3\}, \{1,4\}, \{2,3\}, \{2,4\}, \{3,4\}, \{1,2,3\},
-   \{1,2,4\}, \{1,3,4\}, \{2,3,4\}, \{1,2,3,4\}
+   \{1,2,4\}, \{1,3,4\}, \{2,3,4\}, \{1,2,3,4\}$
 
 * * * *
 
@@ -200,9 +200,9 @@ as the set of points in a circle $C$, the universe would be
 $\Bbb{R}^2$.
 
 **Definition 1.6**
-: $A$ is a set in the universe $U$. The *complement* of $A$ or $A\bar$
-is the set $A\bar = U - A$.
+: $A$ is a set in the universe $U$. The *complement* of $A$ or $\bar A$
+is the set $\bar A = U - A$.
 
 E.g. if $P$ is the set of prime numbers, then $$
-P\bar = \Bbb{N} - P = \{1,4,6,8,9,10,12,\dots\}
-$$ so $P\bar$ is the set of composite numbers and 1.
+\bar P = \Bbb{N} - P = \{1,4,6,8,9,10,12,\dots\}
+$$ so $\bar P$ is the set of composite numbers and 1.