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%=====================================================================================================================================
% Package akkmathset by Igor Akkerman (c) 2000, 2001, 2002, 2003, 2004, 2005
% Package providing utilities for typesetting mathematical sets.
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License (latest version).
%
% The latest version of this license can be found at
% http://www.latex-project.org/lppl.txt
%
% This file may only be distributed together with the full 'AkkTeX' bundle.
%=====================================================================================================================================
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
\ProvidesPackage{akkmathset}[2005/04/30 1.0.0 by Igor Akkerman (c) 2000, 2001, 2002, 2003, 2004 Package providing utilities for typesetting mathematical sets]
%=====================================================================================================================================
\RequirePackage{amsmath}
\RequirePackage{amssymb}
\RequirePackage{amstext}
\RequirePackage{latexsym}
%-----------------------------------------------------------------------------------------------------------------------------------------------------------------------
\newcommand \NN {{\mathbb N}}
\newcommand \NNN {{\NN\minuszero}}
\newcommand \RR {{\mathbb R}}
\newcommand \RRm {\RR^m}
\newcommand \RRn {\RR^n}
\newcommand \QQ {{\mathbb Q}}
\newcommand \ZZ {{\mathbb Z}}
\newcommand \CC {{\mathbb C}}
\newcommand \CCm {\CC^m}
\newcommand \CCn {\CC^n}
\newcommand \KK {{\mathbb K}}
\newcommand \KKm {\KK^m}
\newcommand \KKn {\KK^n}
\newcommand \LL {{\mathbb L}}
\newcommand \BB {{\mathcal B}}
\newcommand \PP {{\mathcal P}}
\newcommand \VV {{\mathcal V}}
\newcommand \CCC {{\mathcal C}}
\newcommand \set[1] {\{#1\}}
\newcommand \Set[1] {\openSet #1 \closeSet}
\newcommand \openSet {\!\left\{\left.}
\newcommand \closeSet {\right.\right\}\!}
\newcommand \setcard[1] {{\left| #1 \right|}}
% `such that' bar
\newcommand \sth {\,|\,}
\newcommand \Sth {\right| \left.}
\newcommand \sm \setminus
\newcommand \setcomp[1] {{\overline{{#1}}}}
\newcommand \C[1] {{\setcomp{#1}}}
\newcommand \zeroset {{\set 0}}
\newcommand \minuszero {{\setminus\zeroset}}
\newcommand \Minuszero {{\!\setminus\!\zeroset}}
\newcommand \mz \minuszero
\newcommand \Mz \Minuszero
\newcommand \pset[1] {{\PP({#1})}}
\newcommand \Pset[1] {{\PP\({#1}\)}}
\newcommand \Abb {{\operatorname{Abb}}}
\newcommand \mker {{\operatorname{ker}}}
\newcommand \Ker {{\operatorname{Ker}}}
\newcommand \Kern {{\operatorname{Kern}}}
\newcommand \Bild {{\operatorname{Bild}}}
\renewcommand \Im {{\operatorname{Im}}}
\newcommand \End {{\operatorname{End}}}
\newcommand \Eig {{\operatorname{Eig}}}
\newcommand \Hom {{\operatorname{Hom}}}
\newcommand \Mat {{\operatorname{Mat}}}
\newcommand \gl {{\operatorname{GL}}}
\newcommand \GL {{\operatorname{GL}}}
\newcommand \mspan[1][] {{\operatorname{span}\ifset{#1}{\Set{#1}}}}
\newcommand \Span [1][] {{\operatorname{Span}\ifset{#1}{\Set{#1}}}}
\newcommand \erz[1] {\bigl[#1\bigr]}
\newcommand \Erz[1] {\left[#1\right]}
\newcommand \closure[1] {{\overline{{#1}}}}
\newcommand \jset {{\set{1,\dots,j}}}
\newcommand \kset {{\set{1,\dots,k}}}
\newcommand \nset {{\set{1,\dots,n}}}
\newcommand \mset {{\set{1,\dots,m}}}
% big set union with limits
\newcommand \Bigcup[1] {{\bigcup\limits_{#1}}}
% big set intersection with limits
\newcommand \Bigcap[1] {{\bigcap\limits_{#1}}}
% equivalence class
\newcommand \equivclass[2][] {{[{#2}]_{{#1}}}}
\newcommand \eqclass[2][] {{\equivclass{1}{2}}}
% quotient set
\newcommand \quot[2] {{{#1}/\!\raisebox{-.575ex}{\ensuremath{#2}}}}
% square set MxM
\newcommand \sqset[1] {#1 \times #1}
\newcommand \sqseta {\sqset A}
\newcommand \sqsetb {\sqset B}
\newcommand \sqsetc {\sqset C}
\newcommand \sqsetcc {\sqset \CC}
\newcommand \sqseti {\sqset I}
\newcommand \sqsetkk {\sqset \KK}
\newcommand \sqsetm {\sqset M}
\newcommand \sqsetnn {\sqset \NN}
\newcommand \sqsetqq {\sqset \QQ}
\newcommand \sqsetr {\sqset R}
\newcommand \sqsetrr {\sqset \RR}
\newcommand \sqsets {\sqset S}
\newcommand \sqsett {\sqset T}
\newcommand \sqsetu {\sqset U}
\newcommand \sqsetv {\sqset V}
\newcommand \sqsetw {\sqset W}
\newcommand \sqsetx {\sqset X}
\newcommand \sqsety {\sqset Y}
\newcommand \sqsetz {\sqset Z}
\newcommand \sqsetzz {\sqset \ZZ}
%------------------------------------------------------------------------------
% families
%------------------------------------------------------------------------------
\newcommand \family[3] {{{\({{#1}_{#2}}\)}_{{#2} \in {#3}}}}
\newcommand \ifam[1] {{\family{#1} i I}}
%------------------------------------------------------------------------------
% elements
%------------------------------------------------------------------------------
\newcommand \nin {{n\in\NN}}
\newcommand \ninn {{n\in\NNN}}
\newcommand \kin {{k\in\NN}}
\newcommand \kinn {{k\in\NNN}}
\newcommand \ini {{i\in I}}
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