X-Git-Url: http://git.subgeniuskitty.com/surreal-numbers/.git/blobdiff_plain/420b03029f815fa5f0dbf6a47764ec7e977a88d1..ef10cd2cd96c1f502a10212f08329d1566b9ebac:/notes/chapter-1.tex

diff --git a/notes/chapter-1.tex b/notes/chapter-1.tex
index aa7751c..9a1e41c 100644
--- 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.
 
-$$\surreal{0}{} = \surreal{-1,0}{}$$
+$$\surreal{0}{} \similar \surreal{-1,0}{}$$
 $$\surreal{}{}$$
-$$\surreal{}{0}, \surreal{}{0,1}$$
+$$\surreal{}{0} \similar \surreal{}{0,1}$$
 $$\surreal{-1}{}$$
-$$\surreal{1}{}, \surreal{0,1}{}, \surreal{-1,1}{}, \surreal{-1,0,1}{}$$
+$$\surreal{1}{} \similar \surreal{0,1}{} \similar \surreal{-1,1}{} \similar \surreal{-1,0,1}{}$$
 $$\surreal{-1}{1}$$
-$$\surreal{0}{1}, \surreal{-1,0}{1}$$
+$$\surreal{0}{1} \similar \surreal{-1,0}{1}$$
 $$\surreal{}{1}$$
-$$\surreal{-1}{0}, \surreal{-1}{0,1}$$
-$$\surreal{}{-1}, \surreal{}{-1,0}, \surreal{}{-1,1}, \surreal{}{-1,0,1}$$
+$$\surreal{-1}{0} \similar \surreal{-1}{0,1}$$
+$$\surreal{}{-1} \similar \surreal{}{-1,0} \similar \surreal{}{-1,1} \similar \surreal{}{-1,0,1}$$
 
 From this we see that, since Axiom \autoref{ax:leq-comparison} makes its
 comparison element-wise, every surreal number generated by our current methods
