From ef10cd2cd96c1f502a10212f08329d1566b9ebac Mon Sep 17 00:00:00 2001 From: Aaron Taylor Date: Tue, 4 May 2021 22:08:41 -0700 Subject: [PATCH] Fixed typo in chapter 1 notes where numbers are similar. --- notes/chapter-1.tex | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) 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 -- 2.20.1