Section 1.3: Functions

Show that the Signum Function \(f : \mathbb{R} \to \mathbb{R}\), given by
\[ f(x) = \begin{cases} 1, & \text{if } x > 0 \\ 0, & \text{if } x = 0 \\ -1, & \text{if } x < 0 \end{cases} \] is neither one-one nor onto.