Bijection between $\mathbb{R} \times \mathbb{R}$ and $\mathbb{R}$

Question

How can we define bijection in between $\mathbb{R} \times \mathbb{R}$ and $\mathbb{R}$? Even giving a injection from $\mathbb{R} \times \mathbb{R}$ to $\mathbb{R}$ and vice-versa will work.

Answer 1

Hint: Find a bijection $\mathbb R\to\mathbb N^{\mathbb N}$ or $\mathbb R\to\mathbb 2^{\mathbb N}$