From 2dddf218c76c61948998ebdf7ed9f69ed13cbeb9 Mon Sep 17 00:00:00 2001
From: Levi Pearson <levi.pearson@harman.com>
Date: Sat, 25 Jan 2014 15:51:10 -0700
Subject: [PATCH] More notes

---
 math/proof/notes.page | 17 +++++++++++++++--
 1 file changed, 15 insertions(+), 2 deletions(-)

diff --git a/math/proof/notes.page b/math/proof/notes.page
index d3d8bc9..393343e 100644
--- a/math/proof/notes.page
+++ b/math/proof/notes.page
@@ -216,15 +216,28 @@ $$ so $\overline P$ is the set of composite numbers and 1.
 
 **Definition 1.7**
 
-$A_1, A_2,\dots, A_n$ are sets.
+$A_1, A_2,\dots, A_n$ are sets. Then
 
 $$\begin{align}
 A_1 \cup A_2 \cup A_3 \cup \dots \cup A_n &=
 \left\{x : x \in A_i
   \text{ for at least one set $A_i$, for }
   1 \leq i \leq n\right\}\\
-A_1 \cap A_2 \cap A_3 \cap \dots \cap A-n &=
+A_1 \cap A_2 \cap A_3 \cap \dots \cap A_n &=
 \left\{x : x \in A_i
   \text{ for every set $A_i$, for }
   1 \leq i \leq n \right\}\\
 \end{align}$$
+
+Given $A_1, A_2, \dots, A_n$ we define
+
+$$\begin{align}
+\bigcup{i=1}{n} A_i &= A_1 \cup A_2 \cup \dots \cup A_n\\
+\bigcap{i=1}{n} A_i &= A_1 \cap A_2 \cap \dots \cap A_n\\
+\end{align}$$
+
+$$
+A_1 = \{-1,0,1}, A_2 = \{-2,0,2}, \dots, A_i = \{-i,0,i}, \dots\\
+\bigcup{i=1}{\inf} A_i = \Bbb{Z} \text{ and }
+\bigcap{i=1}{\inf} A_i = \{0\}\\
+$$