-Challenging question-

Let $\displaystyle c(x)$ define on all real numbers and

$\displaystyle \displaystyle c(x)=\lim_{m\to \infty} \left [\lim_{n\to \infty} \cos^n (\pi m! x)\right ].$

Show that $\displaystyle c(x)$ is nowhere continuous.

I suppose I was sent the solution so that I could approve this, but you are relying on me and/or the other senior staff being psychic rather than the more usual psychotic which as Sir Humphry would say is "Brave". In future try saying why you have sent such material.

Approved CB