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Is there a function which returns $1$ if we give it a positive number and $0$ if we give it a negative number? For example:

$f(-6.3) = 0$

And

$f(6.3) = 1$

Thanks in advance for your answers.

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    The function actually has a name. It is called the unit step function (also the Heaviside step function) and it is useful in areas such as Laplace transforms. https://en.wikipedia.org/wiki/Heaviside_step_function – 2017-02-18

3 Answers 3

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If you would like an equation for the unit step function you could use this:

$$ U(x)=\frac{1}{2}\left(1+\frac{\vert x\vert}{x}\right)$$

This version is undefined for $x=0$.

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    Thank you ! That was exactly what I needed – 2017-02-18
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    You are welcome. – 2017-02-18
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We can have $$f (x) = \begin {cases} 1; x > 0 \\ 0 ; x <0\end {cases} $$

Hope it helps.

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Yes, step function (https://en.m.wikipedia.org/wiki/Step_function).

$ f(x) = 1 $ for $x \geq 0$ and $0$ otherwise.