\usepackage{amsfonts}
\fi
-\ifx\bigtimes\undefined
- \usepackage{mathtools}
-\fi
-
% Place the argument in matching left/right parentheses.
\newcommand*{\of}[1]{ \left({#1}\right) }
% Group terms using square brackets.
\newcommand*{\sqty}[1]{ \left[{#1}\right] }
-% 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}
-
% A pair of things.
\newcommand*{\pair}[2]{ \left({#1},{#2}\right) }
% A seven-tuple of things.
\newcommand*{\septuple}[7]{ \left({#1},{#2},{#3},{#4},{#5},{#6},{#7}\right) }
-% 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 direct sum of two things.
\newcommand*{\directsum}[2]{ {#1}\oplus{#2} }
\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 intersection of its two arguments.
-\newcommand*{\intersect}[2]{ {#1}\cap{#2} }
-
-% A three-argument intersection.
-\newcommand*{\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
{ {#1}_{#2}^{#3}{#4} }
}
-\newcommand*{\intersectmany}[3]{ \binopmany{\bigcap}{#1}{#2}{#3} }
-\newcommand*{\cartprodmany}[3]{ \binopmany{\bigtimes}{#1}{#2}{#3} }
+
\newcommand*{\directsummany}[3]{ \binopmany{\bigoplus}{#1}{#2}{#3} }
-\newcommand*{\unionmany}[3]{ \binopmany{\bigcup}{#1}{#2}{#3} }
+
% The four standard (UNLESS YOU'RE FRENCH) types of intervals along
% the real line.