mjo-set.tex

   1 %
   2 % Things that fit absolutely nowhere else.
   3 %
   4 \ifx\havemjoset\undefined
   5 \def\havemjoset{1}
   6
   7 \input{mjo-common} % binopmany
   8 \input{mjo-font} % amsfonts and \mathpzc
   9
  10 \ifx\operatorname\undefined
  11   \usepackage{amsopn}
  12 \fi
  13
  14 \ifx\bigtimes\undefined
  15   \usepackage{mathtools}
  16 \fi
  17
  18
  19 % The cardinality of a set. The |X| notation conflicts with the
  20 % absolute value, and the meaning of card(X) is clear at once, so we
  21 % prefer the latter.
  22 \newcommand*{\card}[1]{ \operatorname{card}\of{{#1}} }
  23
  24
  25 % The powerset of (that is, the set of all subsets of) its argument.
  26 \newcommand*{\powerset}[1]{\mathpzc{P}\of{{#1}}}
  27 \ifdefined\newglossaryentry
  28   \newglossaryentry{powerset}{
  29     name={\ensuremath{\powerset{X}}},
  30     description={the ``powerset,'' or set of all subsets of $X$},
  31     sort=p
  32   }
  33 \fi
  34
  35
  36 %
  37 % Basic set operations
  38 %
  39
  40 % The union of its two arguments.
  41 \newcommand*{\union}[2]{ {#1}\cup{#2} }
  42
  43 % A three-argument union.
  44 \newcommand*{\unionthree}[3]{ \union{\union{#1}{#2}}{#3} }
  45
  46 % The indexed union of many things.
  47 \newcommand*{\unionmany}[3]{ \binopmany{\bigcup}{#1}{#2}{#3} }
  48
  49 % The intersection of its two arguments.
  50 \newcommand*{\intersect}[2]{ {#1}\cap{#2} }
  51
  52 % A three-argument intersection.
  53 \newcommand*{\intersectthree}[3]{ \intersect{\intersect{#1}{#2}}{#3} }
  54
  55 % The indexed intersection of many things.
  56 \newcommand*{\intersectmany}[3]{ \binopmany{\bigcap}{#1}{#2}{#3} }
  57
  58 % The Cartesian product of two things.
  59 \newcommand*{\cartprod}[2]{ {#1}\times{#2} }
  60
  61 % The Cartesian product of three things.
  62 \newcommand*{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
  63
  64 % The indexed Cartesian product of many things.
  65 \newcommand*{\cartprodmany}[3]{ \binopmany{\bigtimes}{#1}{#2}{#3} }
  66
  67
  68 \fi