-\providecommand*{\intersectmany}[3]{ \binopmany{\bigcap}{#1}{#2}{#3} }
-\providecommand*{\cartprodmany}[3]{ \binopmany{\bigtimes}{#1}{#2}{#3} }
-\providecommand*{\directsummany}[3]{ \binopmany{\bigoplus}{#1}{#2}{#3} }
-\providecommand*{\unionmany}[3]{ \binopmany{\bigcup}{#1}{#2}{#3} }
+\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} }
+
+\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
+
+% The four standard (UNLESS YOU'RE FRENCH) types of intervals along
+% the real line.
+\newcommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
+\newcommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
+\newcommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
+\newcommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed
+
+
+\fi