elementary set theory - Bijection between $mathbb{R}$ and $mathbb{R}^2$

I have been thinking for a while whether its possible to have bijection between $\mathbb{R}$ and $\mathbb{R}^2$, but I cant think of a solution. So my question is: is there a bijection between $\mathbb{R}$ and $\mathbb{R}^2$ (with proof)?

Answer

Yes there is. I think it is one of the results of Cantor. Take two real numbers and combine them by interposing their digit in the decimal expansion.

example:

$$(0.1415\dots,0.7172\dots) \mapsto (0.17411752\dots)$$