I was reading a calculus book and there was this task:
prove that you cannot select a pointwise convergent subsequence from the sequence $$f_n(x) = \sin(nx)$$ consider that it's on $$[0, 1]$$
I've tried to prove it using definition of pointwise convergence, also I used [0, 1] by writing some inequalities for x, but it seems like that's not the way how I can solve it. Can you help me out?
