Show that `f:n->N` defined by `f(n)={(((n+1)/2,(if n is odd)),(n/2,(if n is even))` is many -one onto function

Explanation

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

\[
f(n) =
\begin{cases}
\frac{n + 1}{2} & \text{if } n \text{ is odd} \\
\frac{n}{2} & \text{if } n \text{ is even}
\end{cases}
...