I'm working on this problem that involves the collections of sets. I'm not really sure how to approach this problem. I understand that to prove that something is numerically equivalent one must show that there is a bijection. Any help would be appreciated.
Let $\{A_i\}_{i \in \mathbb{Z_+}}$ be a countable collection of sets. Let $B = \displaystyle \prod_{i\in \mathbb{Z_+}}A_i$ be the Cartesian product of the collection. Prove that if every set of the collection $\{A_i\}_{i\in \mathbb{Z_+}}$ contains two distinct elements, then $B$ is numerically equivalent to $\mathbb{R}$, that is, $|B|=|\mathbb{R}|$