Let `f: Nuu{0}vecNuu{0}` be defined by `f{n+1,if n` is even n-1,if n is odd Show that `f` is a bijection.

Explanation

To show that the function \( f: \mathbb{N} \cup \{0\} \to \mathbb{N} \cup \{0\} \) defined by:

\[
f(n) =
\begin{cases}
n + 1 & \text{if } n \text{ is even} \\
n - 1 & \text{if } n \text{ is odd}
\end{cases}
...