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

I know it's possible to produce a bijection from $\mathbb{Z}$ to $\mathbb{Z}\times\mathbb{Z}$, but is it possible to do so from $\mathbb{R}$ to $\mathbb{R} \times \mathbb{R}$?

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    Yes. Describing one *explicitly* is mildly unpleasant, but it can be done. *Showing* there is a bijection is easier.2012-11-18
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    @Robert: It is possible.2012-11-18
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    The earlier *question* is slightly different, but [this answer](http://math.stackexchange.com/a/183383/12042) to it has everything that’s needed here in considerable detail.2012-11-18

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