Fixed typo in chapter 1 notes where numbers are similar.

diff --git a/notes/chapter-1.tex b/notes/chapter-1.tex
index aa7751c..9a1e41c 100644 (file)
--- a/notes/chapter-1.tex
+++ b/notes/chapter-1.tex
@@ -66,16 +66,16 @@ interchangeably.
 Using this definition, the twenty numbers from generations 0-2 break down into
 ten equivalence classes based on similarity, as shown below.
 
 Using this definition, the twenty numbers from generations 0-2 break down into
 ten equivalence classes based on similarity, as shown below.
 

-$$\surreal{0}{} = \surreal{-1,0}{}$$
+$$\surreal{0}{} \similar \surreal{-1,0}{}$$

 $$\surreal{}{}$$
 $$\surreal{}{}$$

-$$\surreal{}{0}, \surreal{}{0,1}$$
+$$\surreal{}{0} \similar \surreal{}{0,1}$$

 $$\surreal{-1}{}$$
 $$\surreal{-1}{}$$

-$$\surreal{1}{}, \surreal{0,1}{}, \surreal{-1,1}{}, \surreal{-1,0,1}{}$$
+$$\surreal{1}{} \similar \surreal{0,1}{} \similar \surreal{-1,1}{} \similar \surreal{-1,0,1}{}$$

 $$\surreal{-1}{1}$$
 $$\surreal{-1}{1}$$

-$$\surreal{0}{1}, \surreal{-1,0}{1}$$
+$$\surreal{0}{1} \similar \surreal{-1,0}{1}$$

 $$\surreal{}{1}$$
 $$\surreal{}{1}$$

-$$\surreal{-1}{0}, \surreal{-1}{0,1}$$
-$$\surreal{}{-1}, \surreal{}{-1,0}, \surreal{}{-1,1}, \surreal{}{-1,0,1}$$
+$$\surreal{-1}{0} \similar \surreal{-1}{0,1}$$
+$$\surreal{}{-1} \similar \surreal{}{-1,0} \similar \surreal{}{-1,1} \similar \surreal{}{-1,0,1}$$

 
 From this we see that, since Axiom \autoref{ax:leq-comparison} makes its
 comparison element-wise, every surreal number generated by our current methods
 
 From this we see that, since Axiom \autoref{ax:leq-comparison} makes its
 comparison element-wise, every surreal number generated by our current methods