From: Neil Smith <neil.git@njae.me.uk>
Date: Wed, 12 Mar 2014 12:37:20 +0000 (+0000)
Subject: Fixed conflicting equation typesetting
X-Git-Url: https://git.njae.me.uk/?a=commitdiff_plain;h=5b51a469cc152b1035a5cf69f2c38d51f9d16eb8;p=cipher-training.git

Fixed conflicting equation typesetting
---

5b51a469cc152b1035a5cf69f2c38d51f9d16eb8
diff --cc slides/caesar-break.html
index c6d4023,6df8365..a47e236
--- a/slides/caesar-break.html
+++ b/slides/caesar-break.html
@@@ -131,26 -123,19 +149,26 @@@ Counting letters in _War and Peace_ giv
  
  Several different distance measures (__metrics__, also called __norms__):
  
 -* L<sub>2</sub> norm (Euclidean distance):  `\(\|\mathbf{x} - \mathbf{y}\| = \sqrt{\sum_i (\mathbf{x}_i - \mathbf{y}_i)^2} \)`
 +* L<sub>2</sub> norm (Euclidean distance): 
- `\(|\mathbf{a} - \mathbf{b}| = \sqrt{\sum_i (\mathbf{a}_i - \mathbf{b}_i)^2} \)`
++`\(\|\mathbf{a} - \mathbf{b}\| = \sqrt{\sum_i (\mathbf{a}_i - \mathbf{b}_i)^2} \)`
  
 -* L<sub>1</sub> norm (Manhattan distance, taxicab distance):  `\(\|\mathbf{x} - \mathbf{y}\| = \sum_i |\mathbf{x}_i - \mathbf{y}_i| \)`
 +* L<sub>1</sub> norm (Manhattan distance, taxicab distance): 
- `\(|\mathbf{a} - \mathbf{b}| = \sum_i |\mathbf{a}_i - \mathbf{b}_i| \)`
++`\(\|\mathbf{a} - \mathbf{b}\| = \sum_i |\mathbf{a}_i - \mathbf{b}_i| \)`
  
 -* L<sub>3</sub> norm:  `\(\|\mathbf{x} - \mathbf{y}\| = \sqrt[3]{\sum_i |\mathbf{x}_i - \mathbf{y}_i|^3} \)`
 +* L<sub>3</sub> norm: 
- `\(|\mathbf{a} - \mathbf{b}| = \sqrt[3]{\sum_i |\mathbf{a}_i - \mathbf{b}_i|^3} \)`
++`\(\|\mathbf{a} - \mathbf{b}\| = \sqrt[3]{\sum_i |\mathbf{a}_i - \mathbf{b}_i|^3} \)`
  
  The higher the power used, the more weight is given to the largest differences in components.
  
  (Extends out to:
  
 -* L<sub>0</sub> norm (Hamming distance):  `\(\|\mathbf{x} - \mathbf{y}\| = \sum_i \left\{\begin{matrix} 1 &amp;\mbox{if}\ \mathbf{x}_i \neq \mathbf{y}_i , \\ 0 &amp;\mbox{if}\ \mathbf{x}_i = \mathbf{y}_i \end{matrix} \right| \)`
 +* L<sub>0</sub> norm (Hamming distance): 
- `$$|\mathbf{a} - \mathbf{b}| = \sum_i \left\{
++`$$\|\mathbf{a} - \mathbf{b}\| = \sum_i \left\{
 +\begin{matrix} 1 &amp;\mbox{if}\ \mathbf{a}_i \neq \mathbf{b}_i , \\
 + 0 &amp;\mbox{if}\ \mathbf{a}_i = \mathbf{b}_i \end{matrix} \right. $$`
  
 -* L<sub>&infin;</sub> norm:  `\(\|\mathbf{x} - \mathbf{y}\| = \max_i{(\mathbf{x}_i - \mathbf{y}_i)} \)`
 +* L<sub>&infin;</sub> norm: 
- `\(|\mathbf{a} - \mathbf{b}| = \max_i{(\mathbf{a}_i - \mathbf{b}_i)} \)`
++`\(\|\mathbf{a} - \mathbf{b}\| = \max_i{(\mathbf{a}_i - \mathbf{b}_i)} \)`
  
  neither of which will be that useful.)
  ---