Show that $Per_n(f)$ of periodic points of period $n$ is finite

Question

Prove that if $f: X \rightarrow X$ is an expansive topological dynamical system of a compact dynamical system $X$, then the set $Per_n(f)$ of periodic points of period $n$ is finite.

Any ideas of how to approach this question?

Could strong hints be given please.

Answer 1

Hint: suppose $x$ is an accumulation point of $Per_n(f)$. What can you deduce?