Bijection between finite and infinite sequences over Reals.

So define the set of finite sequences to be $S={a_1,a_2,\cdots}$ where $a_k$ are in real numbers and only finitely many of them are non-zero. The set of infinite sequences is defined similarly except that we can have infinitely many non-zero terms. How do I prove that there does not exist a bijection between these two sets?