Functions

A function $f$ from the set of natural numbers to integers defined by

$$f(n)=\left\{\begin{array}{l} \frac{n-1}{2}, \quad \text { when } n \text { is odd } \\ -\frac{n}{2}, \quad \text { when } n \text { is even } \end{array} \quad\right. \text { is }$$