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Fixed typo in chapter 1 notes where numbers are similar.
author
Aaron Taylor
<ataylor@subgeniuskitty.com>
Wed, 5 May 2021 05:08:41 +0000
(22:08 -0700)
committer
Aaron Taylor
<ataylor@subgeniuskitty.com>
Wed, 5 May 2021 05:08:41 +0000
(22:08 -0700)
notes/chapter-1.tex
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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