How could we see that $\{n_k\}_k$ converges $\infty$? Let $x \in \Bbb R\setminus \Bbb Q$ and the sequence $\{\frac {m_k} {n_k}\}_k$  concerges to $x$. The question is from this comment by Ilya:

How could we see that $\{n_k\}_k$ converges $\infty$?

Thanks for your help.

A sequence of integers if it's convergent then its limit is also an integer and in this case the limit of $(\frac{m_k}{n_k})$ is a rational which contradicts the hypothesis so what we can conclude?
