How to prove the Cartesian Product of a set is numerically equivalent to real numbers

Question

Set $A = \{0, 1\}$.

Prove that the set $S=\prod\limits_{i \in Z^+}A$ is numerically equivalent to $R$.

If I understand correctly I need to establish a bijective function between set $S$ and real numbers $R$.

I am very confused about what a Cartesian Product from $i \in Z^+$ implies.

Any hints would be greatly appreciated.