From a290d583ca3c4dfc39115068f209d64449c93a03 Mon Sep 17 00:00:00 2001
From: bnewbold
Date: Sun, 24 Jan 2010 03:39:25 -0500
Subject: math fixes
---
math/sets.page | 51 ++++++++++++++++++++++++++++-----------------------
1 file changed, 28 insertions(+), 23 deletions(-)
(limited to 'math/sets.page')
diff --git a/math/sets.page b/math/sets.page
index 42eb831..7b464ed 100644
--- a/math/sets.page
+++ b/math/sets.page
@@ -1,25 +1,30 @@
-====================
-Sets
-====================
+---
+format: markdown
+categories: math
+toc: no
+...
-.. note:: Most of the definitions and notation in the section are based on [rudin]_ or [meserve]_
+# Sets
-Basics
-=============
-If every element :latex:`$a \in A$` is also :latex:`$a \in B$`, then we call
-A a *subset* of B and write :latex:`$A \subset B$`. If there are elements of B
+*References: Most of the definitions and notation in the section are based on
+[^rudin] or [^meserve]*
+
+## Basics
+
+If every element $a \in A$ is also $a \in B$, then we call
+A a *subset* of B and write $A \subset B$. If there are elements of B
which are not elements of A, then we call A a *proper subset* of B.
-If :latex:`$A \supset B$` and :latex:`$B \supset A$` we write :latex:`$A = B$`;
-otherwise :latex:`$A \neq B$`.
+If $A \supset B$ and $B \supset A$ we write $A = B$;
+otherwise $A \neq B$.
The null or empty set, which has no elements, is a subset of all others.
A relation on a space of sets S is something that can be definted as either
true or false (holding or not holding) for any binary pair in S.
-Binary Operators
-==================
+# Binary Operators
+
Binary operators defined on a set apply to any two elements of that set; order
may or may not be important. A set is *closed* with regards to a binary
operator if it contains the result of the binary operator. A set is *uniquely
@@ -28,20 +33,20 @@ elements of the set is unique from the results from all other pairs of
elements.
Some equivalence relations are
-:latex:`$\identity$` (NOTE: = with three lines) (*identity*);
-:latex:`$\congruence$` (NOTE: = with tilde on top) (*congruence*; eg of
+$\identity$ (NOTE: = with three lines) (*identity*);
+$\congruence$ (NOTE: = with tilde on top) (*congruence*; eg of
geometric figures); and
-:latex:`$~$` (NOTE: tilde) (*similarity*; eg of geometric figures).
+$~$ (NOTE: tilde) (*similarity*; eg of geometric figures).
Some properties of equivalence relations are
-*reflexive*
- if :latex:`$a=a$` is true for all a
-*symetric*
- if :latex:`$a=b$` implies :latex:`$b=a$`
-*transitive*
- if :latex:`$a=b$` and :latex:`$b=c$` implies :latex:`$a=c$`
+reflexive
+ if $a=a$ is true for all a
+symetric
+ if $a=b$ implies $b=a$
+transitive
+ if $a=b$ and $b=c$ implies $a=c$
-.. [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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