Asymptotic Growth of Euler Phi Function

Theorem
Let $\phi$ be the Euler's function

For any $\epsilon > 0$ and sufficiently large $n$ we have:


 * $n^{1-\epsilon} < \phi(n) < n$

Proof
It is clear that $\phi(n) < n$ for all $n$, so it is sufficient to prove that:


 * $\displaystyle \lim_{n \to \infty} \frac{n^{1-\epsilon}}{\phi(n)} = 0$