6. Let $a \geqslant 2$ be a given positive integer. Prove:
(i) For any positive integer $n$, there must be $n < a^{n}$;
(ii) For any positive integer $n$, there must be a unique integer $k \geqslant 0$, such that $a^{k} \leqslant n < a^{k+1}$.