ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
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Deduction system
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Zermelo-Fraenkel set theory
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Real collection function
Euclidean real function
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Indicator function
Definition D109
Signum function
Formulation 0
The signum function is the D4948: Integer function \begin{equation} \mathbb{R} \to \{ -1, 0, 1 \}, \quad I_{(0, \infty)} (x) - I_{(-\infty, 0)} (x) \end{equation}
Formulation 1
The signum function is the D4948: Integer function \begin{equation} \mathbb{R} \to \{ -1, 0, 1 \}, \quad I_{x \in (0, \infty)} - I_{x \in (-\infty, 0)} \end{equation}
Formulation 2
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}