Prove that set is countable?

Question

Show that the set N* of finite sequences of nonnegative integers is countable.

Where do I start? I think I have to prove that there is a bijection between N* and N (set of natural numbers), but how do I get there?

Answer 1

Think about the function that sends a sequence $(a_1,a_2,a_3,\ldots,a_n)$ to $2^{a_1} 3^{a_2} 5^{a_3}\ldots p_n^{a_n}$, where $p_n$ denotes the $n$-th prime number.