From: Jim Pryor <profjim@jimpryor.net>
Date: Fri, 17 Sep 2010 01:50:19 +0000 (-0400)
Subject: fix multiplication
X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=7ef19584ac9af6335037790ce1e59172e0ec14fc

fix multiplication

Signed-off-by: Jim Pryor <profjim@jimpryor.net>
---

diff --git a/lists_and_numbers.mdwn b/lists_and_numbers.mdwn
index 2f59e263..17b6dfd8 100644
--- a/lists_and_numbers.mdwn
+++ b/lists_and_numbers.mdwn
@@ -295,12 +295,16 @@ Perhaps not as elegant as addition, but still decently principled.
 
 Multiplication is even more elegant. Consider that applying an arbitrary function s to a base value z *m &times; n* times is a matter of applying s to z *n* times, and then doing that again, and again, and so on...for *m* repetitions. In other words, it's a matter of applying the function (\z. n s z) to z *m* times. In other words, *m &times; n* can be represented as:
 
-<pre><code>    \s z. m (\z. n s z) z
-~~> \s z. m n s z</code></pre>
+	\s z. m (\z. n s z) z
 
-which eta-reduces to:
+which, doing an eta-reduction and permitting ourselves the `&#8728;` notation, is:
+
+<pre><code>\s z. (m &#8728; n) s z</code></pre>
+
+and some more eta-reduction gives us:
+
+<pre><code>m &#8728; n</code></pre>
 
-	m n
 
 Isn't that nice?