update notations and fix typos

pages/Math4111/Math4111_L3.md

@@ -22,10 +22,12 @@ Let $S=\mathbb{Z}$.
 
 ## Continue
 
-### LUBP
+### LUBP (The least upper bound property)
 
 Proof that $LUBP\implies GLBP$.
 
+Proof:
+
 Let $S$ be an ordered set with LUBP. Let $B<S$ be non-empty and bounded below.
 
 Let $L=y\in S:y$ is a lower bound of $B$. From the picture, we expect $\sup L=\inf B$ First we'll show $\sup L$ exists.
@@ -55,6 +57,8 @@ Let's say $\alpha=sup\ L$. We claim that $\alpha=inf\ B$. We need to show $2$ th
 
 Thus $\alpha=inf\ B$
 
+QED
+
 ### Field
 
 |                | addition                                                    | multiplication                                                 |