X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-set.tex;h=4177f5aae68e5103624821d64b202a3f04ff7348;hp=6addd605537bcbb696e502347072613a25faa090;hb=HEAD;hpb=83458c3f65b80a7897ced0553804b38f4872fcb6

diff --git a/mjo-set.tex b/mjo-set.tex
index 6addd60..66cd56b 100644
--- a/mjo-set.tex
+++ b/mjo-set.tex
@@ -4,15 +4,74 @@
 \ifx\havemjoset\undefined
 \def\havemjoset{1}
 
+\input{mjo-common} % binopmany
+\input{mjo-font} % amsfonts and \mathpzc
 
 \ifx\operatorname\undefined
   \usepackage{amsopn}
 \fi
 
+\ifx\bigtimes\undefined
+  \usepackage{mathtools}
+\fi
+
+% Create a set from the given elements
+\newcommand*{\set}[1]{\left\lbrace{#1}\right\rbrace}
+
+% A set comprehension, where the ``such that...'' bar is added
+% automatically. The bar was chosen over a colon to avoid ambiguity
+% with the L : V -> V notation. We can't leverage \set here because \middle
+% needs \left and \right present.
+\newcommand*{\setc}[2]{\left\lbrace{#1}\ \middle|\ {#2}\right\rbrace}
+
+
 % The cardinality of a set. The |X| notation conflicts with the
 % absolute value, and the meaning of card(X) is clear at once, so we
 % prefer the latter.
-\newcommand*{\card}[1]{ \operatorname{card} \of{{#1}} }
+\newcommand*{\card}[1]{ \operatorname{card}\of{{#1}} }
+
+
+% The powerset of (that is, the set of all subsets of) its argument.
+\newcommand*{\powerset}[1]{\mathpzc{P}\of{{#1}}}
+\ifdefined\newglossaryentry
+  \newglossaryentry{powerset}{
+    name={\ensuremath{\powerset{X}}},
+    description={the ``powerset,'' or set of all subsets of $X$},
+    sort=p
+  }
+\fi
+
+
+%
+% Basic set operations
+%
+
+% The union of its two arguments.
+\newcommand*{\union}[2]{ {#1}\cup{#2} }
+
+% A three-argument union.
+\newcommand*{\unionthree}[3]{ \union{\union{#1}{#2}}{#3} }
+
+% The indexed union of many things.
+\newcommand*{\unionmany}[3]{ \binopmany{\bigcup}{#1}{#2}{#3} }
+
+% The intersection of its two arguments.
+\newcommand*{\intersect}[2]{ {#1}\cap{#2} }
+
+% A three-argument intersection.
+\newcommand*{\intersectthree}[3]{ \intersect{\intersect{#1}{#2}}{#3} }
+
+% The indexed intersection of many things.
+\newcommand*{\intersectmany}[3]{ \binopmany{\bigcap}{#1}{#2}{#3} }
+
+% The Cartesian product of two things.
+\newcommand*{\cartprod}[2]{ {#1}\times{#2} }
+
+% The Cartesian product of three things.
+\newcommand*{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
+
+% The indexed Cartesian product of many things.
+\newcommand*{\cartprodmany}[3]{ \binopmany{\bigtimes}{#1}{#2}{#3} }
 
 
 \fi