From f61026119df4700f69eb73e95620bc5928ca0fcb Mon Sep 17 00:00:00 2001
From: User <bnewbold@daemon.robocracy.org>
Date: Tue, 13 Oct 2009 02:52:09 +0000
Subject: Grand rename for gitit transfer

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+====================
+Algebra
+====================
+
+.. note:: Most of the definitions and notation in the section are based on [rudin]_ or [meserve]_
+
+.. list-table:: Closure of binary operators on given sets of numbers
+
+   * - Operation name
+     - addition
+     - product
+     - subtraction
+     - division
+     - power
+     - root
+   * - Operation symbol
+     - :latex:`$a + b$`
+     - :latex:`$a\times b$`
+     - :latex:`$a-b$`
+     - :latex:`$\frac{a}{b}$`
+     - :latex:`$a^b$`
+     - :latex:`$\sqrt{\text{a}}$`
+   * - Positive Integers
+     - Y
+     - Y
+     - N
+     - N
+     - Y
+     - N
+   * - Positive rationals
+     - Y
+     - Y
+     - N
+     - Y
+     - Y
+     - N
+   * - Rationals (and zero)
+     - Y
+     - Y
+     - Y
+     - Y
+     - Y
+     - N
+   * - Reals wrt positive integers
+     - Y
+     - Y
+     - Y
+     - Y
+     - Y
+     - Y
+   * - Complex numbers
+     - Y
+     - Y
+     - Y
+     - Y
+     - Y
+     - Y
+
+Definitions
+=============
+
+*involution*
+    to raise a number to a given power
+
+*evolution*
+    to take a given root of a number
+
+*associative*
+    :latex:`$(a+b)+c=a+(b+c)$`
+
+*comutative*
+    :latex:`$a+b=b+c$`
+
+*distributive*
+    :latex:`$(a+b)c=ac+bc$`
+
+.. [rudin] `Principles of Mathematical Analysis (3rd ed)`:title:, by Walter Rudin. McGraw-Hill, 1976
+
+.. [meserve] `Fundamental Concepts of Algebra`:title:, by Bruce Meserve.
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