Motivated by a recent MSE [question][1] about the sequence of function $\cos(n!\pi x)$, I have read related several related questions:

 - http://mathoverflow.net/questions/34369/on-the-behaviour-of-sinn-pi-x-when-x-is-irrational
 - [Is there a limit of cos (n!)?](https://math.stackexchange.com/q/8690/9464)


Is the existence of $\lim_{n\to\infty}\cos(n!\pi x)$ for given arbitrary irrational $x$ still an open problem? Are there any known related references/results for this question?


  [1]: https://math.stackexchange.com/q/2071683/9464