$f : \mathbb{N} \to \mathbb{Z}$ is given by $f(n) = \frac{n}{2}$ when $n$ is even and $f(n) = -\frac{n - 1}{2}$ when $n$ is odd. Which of these describes $f$?

Explanation

1. 01

   Even $n$ give the positive integers $1, 2, 3, \ldots$; odd $n$ give $0, -1, -2, \ldots$. The two lists never meet, and within each, different $n$ give different values: one-one.

2. 02

   Any $m > 0$ is $f(2m)$, and any $m \le 0$ is $f(1 - 2m)$: onto. So $f$ is a bijection.