Symbols:S/Signum Function
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Signum Function
- $\map \sgn x$
Let $X \subseteq \R$ be a subset of the real numbers.
The signum function $\sgn: X \to \set {-1, 0, 1}$ is defined as:
- $\forall x \in X: \map \sgn x := \sqbrk {x > 0} - \sqbrk {x < 0}$
where $\sqbrk {x > 0}$ etc. denotes Iverson's convention.
That is:
- $\forall x \in X: \map \sgn x := \begin {cases} -1 & : x < 0 \\ 0 & : x = 0 \\ 1 & : x > 0 \end {cases}$
The $\LaTeX$ code for \(\map \sgn x\) is \map \sgn x
.
Sources
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: The Symmetric Groups: $\S 81$
- 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) ... (previous) ... (next): Frontispiece
- 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) ... (previous) ... (next): Chapter $4$: Notation for some useful Functions: Summary of special symbols: Table $4.1$ Special symbols
- 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) ... (previous) ... (next): Inside Back Cover
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): sgn
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): sgn