# A calculus of the absurd

##### 4.8.2 As a function

One way to define the modulus function is, well, as a function. As the function always needs to be positive, we can write that

$$\abs {x} = \begin{cases} x & x \geqq 0 \\ -1 \cdot x & x < 0 \end {cases}$$

What this means is that in the case where $$x$$ (the input to the modulus function) is bigger than zero, we just return $$x$$. If $$x$$ is smaller than zero, we multiply it by $$-1$$ in order to make it positive.