% custom commands go here %
 
\newcommand{\N}{\mathbb{N}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\K}{\mathbb{K}}
\newcommand{\Q}{\mathbb{Q}}

\newcommand{\Rq}{\R^2}
\newcommand{\Qq}{\Q^2}

\newcommand{\lrarr}{\leftrightarrow}
\newcommand{\larr}{\leftarrow}
\newcommand{\rarr}{\rightarrow}
\newcommand{\Lrarr}{\Leftrightarrow}
\newcommand{\Larr}{\Leftarrow}
\newcommand{\Rarr}{\Rightarrow}

\newcommand{\ex}{\emph{Beispiel: }}
\newcommand{\anm}{\emph{Anmerkung: }}

\newcommand{\linf}{\lim\limits_{n \rightarrow{} \infty}}

%running fraction with slash - requires math mode.
\newcommand*\rfrac[2]{{}^{#1}\!/_{#2}}

% Vector
\newcommand*\colvec[3][]{
	\begin{pmatrix}\ifx\relax#1\relax\else#1\\\fi#2\\#3\end{pmatrix}
}
\newcommand{\xyvec}{\colvec{x}{y}}

% Index command to show the key emphasized
\newcommand{\idx}[1]{{\emph{#1}\index{#1}}}