Limit problem involving bijective function Let $f: \Bbb N^{\star}\to \Bbb N^{\star}$ a bijective functions such that exists $$\lim _{n \to \infty} {\frac {f(n)} {n}}.$$ Find the value of this limit.
I noticed that, if $f(n)=n$, then the limit is $1$. I couldn't make more progress. Can you help me?

Because this limit is finite, exist $M$ and $n_0$ such that $f(n)/n<M$ for all $n>n_0$ ie is bounded ae.
Now, because $f(n)<Mn $ for all $n>n_0$ then $f=O(n)$ and by definition the limit request is 1
