Question

What's a simple example of a bijection of \(\mathbb R \rightarrow \mathbb R^2\)? How about for \(\mathbb R \rightarrow \mathbb R^n\)?

Answer 1

http://en.wikipedia.org/wiki/Space-filling_curve
http://en.wikipedia.org/wiki/Hilbert_curve
http://en.wikipedia.org/wiki/Cantor%E2%80%93Bernstein%E2%80%93Schroeder_theorem
might be helpful to you ... though i don't understand them .. :P

Answer 2

I know about space-filling curves at least... though I'm looking for something more algebraic and quantitative over qualitative. Thanks, though. :-)