% 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}! }
+
%
% Product spaces
%