Prove $\lim_{a \to \infty} \frac{\sin a}{a} = 0$.
Attempt:
$|\frac{\sin a}{a} - 0| \leq |\frac{1}{a}|$ so $\frac{1}{a} < \epsilon \implies a > \frac{1}{\epsilon} $
So $\forall \epsilon > 0 \exists N=\frac{1}{\epsilon} : \forall a> N \implies |\frac{\sin a}{a} - 0| \leq |\frac{1}{a}| = \frac{1}{a} < \epsilon $ which means $\lim_{a \to \infty} \frac{\sin a}{a} = 0$
Is my proof correct?