# Bijection between $\mathbb{R}\times\mathbb{R}$ and $\mathbb{R}$ [duplicate]

It must be posted somewhere, but I can't find it. I've been working on it for a while too without getting anywhere. Does there exist a bijection between $\mathbb{R}\times\mathbb{R}$ and $\mathbb{R}$? Is it possible to give an explicit bijection?

NOTE: This question is not a duplicate of the link suggested. Please see comments for further detail.

## marked as duplicate by Zev Chonoles, Lord_Farin, Pedro Tamaroff♦, Amzoti, Ma MingJun 21 '13 at 21:54

• Yes, there is a isomorphism as vector spaces over $\mathbb{Q}$. – user40276 Jun 21 '13 at 21:24