Do bijective functions exist that map from a function of one dimension to a function of another dimension? For example, does there exist a function $f : \mathbb{R^2} \rightarrow \mathbb{R^3}$ that is bijective? If so, would you please provide an example? If not, how is it possible to prove why this is not possible?
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Yes, because $\mathbb{R}^n$ has the same cardinality as $\mathbb{R}$ for all $n \ge 1$. – Jun 10 '14 at 23:12
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Wam, bam! Enjoy the gold badge. – Git Gud Jun 10 '14 at 23:13
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@Git Gud: I have been enjoying it, thank you. With the exception of two-three times that I was uncertain of my vote, and one time that I misread the question and immediately reopened it. – Asaf Karagila Jun 10 '14 at 23:15