They're also isomorphic as abelian groups under addition. At least if you assume the axiom of choice. See eg. http://math.stackexchange.com/questions/925706/i

They're also isomorphic as abelian groups under addition. At least if you assume the axiom of choice. See eg. http://math.stackexchange.com/questions/925706/is-it-true-that-group-of-real-numbers-under-addition-isomorphic-to-group-of-comp/925723#925723 http://math.stackexchange.com/questions/925706/is-it-true-th...