fixes

1 files changed, 17 insertions, 16 deletions

diff --git a/math/numbers.page b/math/numbers.page
index 6481c75..3e9473e 100644
--- a/math/numbers.page
+++ b/math/numbers.page
@@ -1,27 +1,25 @@
----
-format: markdown
-categories: math
-toc: no
-...
+Numbers
+==========
 
-# Numbers
 
-
-*References: most of the definitions and notation in the section are based on [rudin] or [meserve]*
+*References: most of the definitions and notation in the section are based on [^rudin] or [^meserve]*
 
 incommensurable
-    objects are incommensurable when their ratio isn't rational
+:    objects are incommensurable when their ratio isn't rational
 
-## Real Numbers
+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 Transcendental Numbers
+--------------------------------------
 
 *Algebraic numbers* are solutions of polynomials, such as x in
 $a_0 x^n + a_1 x^{n-1} + a_2 x^{n-2} + ... a_n = 0$, where all a are
@@ -34,12 +32,15 @@ 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?
+Exercise: is the square root of 5 algebraic or transcendental?
+
+$e$
+----------
 
-## e
 $e = \lim_{x \rightarrow 0} (1+x)^{\frac{1}{x}}$
 
-## Infinities
+Infinities
+----------
 
 *aleph-zero* ($\aleph_0$) is the countably infinite set.
 
@@ -47,6 +48,6 @@ Positive integers, integers, and rational numbers are all countably infinite.
 
 It is unproven that the real numbers are *aleph-one* ($\aleph_1$).
 
-[^rudin] **Principles of Mathematical Analysis (3rd ed)**, by Walter Rudin. McGraw-Hill, 1976
+[^rudin]: **Principles of Mathematical Analysis (3rd ed)**, by Walter Rudin. McGraw-Hill, 1976
 
 [^meserve]: **Fundamental Concepts of Algebra**, by Bruce Meserve.