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-rw-r--r--math/numbers.page33
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.