The signum function is the D4948: Integer function \begin{equation} \mathbb{R} \to \{ -1, 0, 1 \}, \quad x \mapsto \begin{cases} 1, \quad & x \in (0, \infty) \\ -1, \quad & x \in (-\infty, 0) \\ 0, \quad & x = 0 \end{cases} \end{equation}