We all know that $f(x)=\sin(x^2)$ is not periodic, so I want to strengthen the proposition to any function which has a minimum positive period.
My idea is that let $f(0)=0$, and we can find all the zero points in $[0,T]$. I tried to prove that the zero points are dense and maybe we can find a contradiction.
Maybe there is a counterexample. I'm not sure about it.
