Show that `f\ : NvecN ,\ ` given by `f(x)={x+,\ \ \ \ \ \ \ \ \ \ \ \ \ if\ x\ i s\ od dx-1,\ \ if\ x\ i s\ e v e n` is both one-one and onto.

Explanation

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

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