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Signum function

The signum function, denoted $\text{sgn}(x)$, is equal to \[\begin{cases} 1 & \text{for } x > 0,\\ -1 & \text{for } x < 0, \\ 0 & \text{for } x=0.\end{cases}\]

Properties

  • The signum function is odd.
  • $\text{sgn}(x)$ is equal to $\frac{|x|}{x}$ for $x \neq 0$.

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