Possible Duplicate:

bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$

Do the real numbers and the complex numbers have the same cardinality?

Does $\mathbb R^2$ contain more numbers than $\mathbb R^1$? I know that there are the same number of even integers as integers, but those are both countable sets. Does the same type of argument apply to uncountable sets? If there exists a 1-1 mapping from $\mathbb R^2$ to $\mathbb R^1$, would that mean that 2 real-valued parameters could be encoded as a single real-valued parameter?