Possible Duplicate:

AC in group isomorphism between R and R^2

Somewhere, I recall being told that there is an isomorphism between $\mathbb{R}$ and $\mathbb{C}$ under addition. However, despite a rather lengthy search, I have been unable to find anything to support this fact, although Paul Yale of Pomona College, in his paper, "Automorphisms of the Complex Numbers," showed that there are "wild" automorphisms of $\mathbb{C}$ that require the axiom of choice to construct. Given that rather surprising fact, it does not seem too unlikely that there could be an isomorphism between $\mathbb{R}$ and $\mathbb{C}$. So, the question is: Is it possible for there to be an isomorphism between $\mathbb{R}$ and $\mathbb{C}$, and if so, what is is?

abelian groups, then the answer is yes: both are in fact $\mathbb Q$-vector spaces of the same dimension, so they are isomorphic as such. – Mariano Suárez-Alvarez♦ Jul 10 '10 at 12:43