update notations and fix typos

pages/Math4111/Math4111_L5.md

@@ -94,6 +94,8 @@ So want $k\leq \frac{y^n-x}{ny^{n-1}}$
 
 [For actual proof, see the text.]
 
+QED
+
 ### Complex numbers
 
 1. $=\{a+bi:a,b\in \mathbb{R}\}$.
@@ -149,7 +151,9 @@ $$
 (\sum a_j b_j)^2=(\sum a_j^2)(\sum b_j^2)
 $$
 
-Proof for real numbers:
+Proof:
+
+For real numbers:
 
 Let $A=\sum a_j^2,B=\sum b_j^2, C=\sum a_j b_j$, want to show $C^2\leq AB$
 
@@ -165,6 +169,8 @@ let $t=C/B$ to get $0\leq A-2(C/B)C+(C/B)^2B=A-\frac{C^2}{B}$
 
 to generalize this to $\mathbb{C}$, $A=\sum |a_j|^2,B=\sum |b_j|^2,C=\sum |a_j \bar{b_j}|$.
 
+QED
+
 ### Euclidean spaces
 
 Nothing much to say. lol.