LaTeX Forum

 \section{Elementarfunktionen}
\noindent \textbf{Identität:}\\
\begin{tabular}{||r|}\hline
id\textsubscript{A}: A $\rightarrow$ A \\
x $\rightarrow$ x. \\
\hline 
\end{tabular} \\\\
\noindent \textbf{Betrag und Vorzeichen:} \\
\begin{tabular}{||l|l||}\hline 
abs: $\mathbb {R}$ $\rightarrow$ $\mathbb {R_0^+}$ \\
$x$ $\rightarrow$ abs $(x)$ := f(x) = |x| = 
\begin{cases}
$-x | x < 0$ \\\
$0 | x = 0$ \\\
$x | x > 0.$
\end{cases} 
&sgn : $\mathbb {R}$ $\rightarrow$ \{-1, 0 , 1\} \\\
&$x$ $\mapsto$ sgn$(x)$ : = 
\begin{cases}
 $-1 | x < 0$ \\\
 $0 | x = 0$ \\\
$1 | x > 0$ \\
\end{cases} \\\hline
\end{tabular} 

\end{document}

\documentclass{article}
\usepackage{mathtools}
\usepackage{amssymb}
\begin{document}
\begin{tabular}{||l|l||}
\hline
$\text{abs : }\mathbb {R}\rightarrow \mathbb {R_0^+}$ &$\text{sgn : }\mathbb {R}\rightarrow \{-1, 0 , 1\}$ \\
&~\\%für das Loch
 $x\rightarrow \text{ abs } (x) := f(x) = |x| = 
 \begin{cases} 
 -x | x < 0 \\ 
 0 | x = 0 \\ 
 x | x > 0. 
 \end{cases}$ & $x \mapsto \text{ sgn }(x)  : = 
\begin{cases} 
 -1 | x < 0 \\\ 
 0 | x = 0 \\\ 
 1 | x > 0 \\ 
 \end{cases}$
 \\
 \hline 
 \end{tabular} 
 \end{document}

\noindent \textbf{Identität:}\\