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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 math/sets | 47 -----------------------------------------------
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 delete mode 100644 math/sets

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-====================
-Sets
-====================
-
-.. note:: Most of the definitions and notation in the section are based on [rudin]_ or [meserve]_
-
-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
-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:`$A \neq B$`.
-
-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 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
-defined* with regards to a binary operator if the result of the operator on two
-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 
-geometric figures); and 
-:latex:`$~$` (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:`$a=c$`
-
-.. [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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