I have seen this question already, and that's not what I'm asking. I would like to know if there is a bijective map between the interval $(-1,1) \rightarrow \mathbb{R}^2$; ie, is there a function that will take a pair $(a,b) \in \mathbb{R}^2$ and give me a unique number in $(-1,1)$. I would also like to know if this is also possible for $[-1,1] \rightarrow \mathbb{R}^2$. Thank you!
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3The answer to the question already gives a bijection $\mathbb R^2 \to \mathbb R$. Invert it to get a bijection $\mathbb R \to \mathbb R^2$. Then find a bijection $(-1, 1) \to \mathbb R$ which is relatively easy and compose to finish. – balddraz May 10 '23 at 00:02
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1In both cases the cardinalities are the same. – geetha290krm May 10 '23 at 00:06
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@ayeayemaung Thank you! – fractal_girl May 10 '23 at 00:13