% A pair of things.
\providecommand*{\pair}[2]{ \left({#1},{#2}\right) }
+% A triple of things.
+\providecommand*{\triple}[3]{ \left({#1},{#2},{#3}\right) }
+
% The Cartesian product of two things.
\providecommand*{\cartprod}[2]{ {#1}\times{#2} }
% The Cartesian product of three things.
\providecommand*{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
+% The direct sum of two things.
+\providecommand*{\directsum}[2]{ {#1}\oplus{#2} }
+
% The factorial operator.
\providecommand*{\factorial}[1]{ {#1}! }
\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} }