X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-common.tex;h=5c0162a76b575e8336bad47740cdeec47f90d1c7;hp=efa10a26045d9f199bd3bdb1f8c9f5ec97c1cb19;hb=eaa1f615a11b7010088cb848ce909c47beb3fb4d;hpb=d84c704c13a2e30c232710801c5483059094dac3

diff --git a/mjo-common.tex b/mjo-common.tex
index efa10a2..5c0162a 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -2,6 +2,9 @@
 % Only the most commonly-used macros. Needed by everything else.
 %
 
+% Needed for \mathbb.
+\usepackage{amsfonts}
+
 % Place the argument in matching left/right parntheses.
 \providecommand*{\of}[1]{ \left({#1}\right) }
 
@@ -71,3 +74,37 @@
 \providecommand*{\Cn}[1][n]{
   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 }
+
+
+%
+% Basic set operations
+%
+
+% The union of its two arguments.
+\providecommand*{\union}[2]{ {#1} \cup {#2} }
+
+% A three-argument union.
+\providecommand*{\unionthree}[3]{ \union{\union{#1}{#2}}{#3} }
+
+% The intersection of its two arguments.
+\providecommand*{\intersect}[2]{ {#1} \cap {#2} }
+
+% A three-argument intersection.
+\providecommand*{\intersectthree}[3]{ \intersect{\intersect{#1}{#2}}{#3} }
+
+% An indexed arbitrary binary operation such as the union or
+% intersection of an infinite number of sets. The first argument is
+% the operator symbol to use, such as \cup for a union. The second
+% argument is the lower index, for example k=1. The third argument is
+% the upper index, such as \infty. Finally the fourth argument should
+% contain the things (e.g. indexed sets) to be operated on.
+\providecommand*{\binopmany}[4]{
+  \mathchoice
+  { \underset{#2}{\overset{#3}{#1}}{#4} }
+  { {#1}_{#2}^{#3}{#4} }
+  { {#1}_{#2}^{#3}{#4} }
+  { {#1}_{#2}^{#3}{#4} }
+}
+
+\providecommand*{\unionmany}[3]{ \binopmany{\cup}{#1}{#2}{#3} }
+\providecommand*{\intersectmany}[3]{ \binopmany{\cap}{#1}{#2}{#3} }