Let pi is a cycle in S(n) of length r. Prove that ord(pi) = r.
TPH meant that if you take any element $\displaystyle \pi \in S_n$ of length r, and if you compose $\displaystyle \pi$ r times, that is, $\displaystyle \underbrace{\pi \pi ... \pi}_{r \, times}$, then you will get $\displaystyle (1)$, the identity.. hence, the order is r..