From a290d583ca3c4dfc39115068f209d64449c93a03 Mon Sep 17 00:00:00 2001
From: bnewbold <bnewbold@ziggy.(none)>
Date: Sun, 24 Jan 2010 03:39:25 -0500
Subject: math fixes

---
 math/numbers.page | 54 ++++++++++++++++++++++++++----------------------------
 1 file changed, 26 insertions(+), 28 deletions(-)

(limited to 'math/numbers.page')

diff --git a/math/numbers.page b/math/numbers.page
index 541d174..6481c75 100644
--- a/math/numbers.page
+++ b/math/numbers.page
@@ -1,54 +1,52 @@
-========================
-Numbers
-========================
+---
+format: markdown
+categories: math
+toc: no
+...
 
-.. note::
-    incomplete
+# Numbers
 
-.. note:: 
-    Most of the definitions and notation in the section are based on [rudin]_ or [meserve]_
 
-.. contents::
+*References: most of the definitions and notation in the section are based on [rudin] or [meserve]*
 
-*incommensurable*
+incommensurable
     objects are incommensurable when their ratio isn't rational
 
-Real Numbers
-==================
-The *real numbers* are defined via Dedakind cuts in [rudin]_, or [meserve]_ 
-(1-12).
+## Real Numbers
+
+The *real numbers* are defined via Dedakind cuts in [^rudin], or [^meserve] 
+(p1-12).
+
+## Complex Numbers
 
-Complex Numbers
-==================
 The *complex numbers* are constructed as an ordered pair of real numbers.
 
-Algebraic and Transendental Numbers
-===============================================
+## Algebraic and Transendental Numbers
+
 *Algebraic numbers* are solutions of polynomials, such as x in
-:latex:`$a_0 x^n + a_1 x^{n-1} + a_2 x^{n-2} + ... a_n = 0$`, where all a are
+$a_0 x^n + a_1 x^{n-1} + a_2 x^{n-2} + ... a_n = 0$, where all a are
 real numbers. *Transcendental numbers* are not solutions to any such 
 polynomials.
 
 All real numbers are either algebraic or transcendental. 
 
-Some algebraic numbers aren't real (such as :latex:`$i = \sqrt{-1}$`). They
+Some algebraic numbers aren't real (such as $i = \sqrt{-1}$). They
 can be rational or irrational. All transcendental numbers are irrational;
 some are not real.
 
 Exersize: is the square root of 5 algebraic or transcendental?
 
-e
-========
-:latex:`$e = \lim_{x \rightarrow 0} (1+x)^{\frac{1}{x}}$`
+## e
+$e = \lim_{x \rightarrow 0} (1+x)^{\frac{1}{x}}$
+
+## Infinities
 
-Infinities
-==================
-*aleph-zero* (:latex:`$\aleph_0$`) is the countably infinite set.
+*aleph-zero* ($\aleph_0$) is the countably infinite set.
 
 Positive integers, integers, and rational numbers are all countably infinite.
 
-It is unproven that the real numbers are *aleph-one* (:latex:`$\aleph_1$`).
+It is unproven that the real numbers are *aleph-one* ($\aleph_1$).
 
-.. [rudin] `Principles of Mathematical Analysis (3rd ed)`:title:, by Walter Rudin. McGraw-Hill, 1976
+[^rudin] **Principles of Mathematical Analysis (3rd ed)**, by Walter Rudin. McGraw-Hill, 1976
 
-.. [meserve] `Fundamental Concepts of Algebra`:title:, by Bruce Meserve.
+[^meserve]: **Fundamental Concepts of Algebra**, by Bruce Meserve.
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