Bijective function from $\Bbb R$ to $\Bbb R^2$

Asked Jun 13 '18 at 05:36

Active Jun 13 '18 at 15:31

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I know that $\Bbb R$ has the same cardinality as $\Bbb R^2$, but can someone give me a bijective or even just a surjective function $f:\Bbb R \to \Bbb R^2$?

edited Jun 13 '18 at 15:31

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asked Jun 13 '18 at 05:36

yes

2

https://en.m.wikipedia.org/wiki/Space-filling_curve – N8tron Jun 13 '18 at 05:40
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See https://math.stackexchange.com/q/243590/513123 – P.Diddy Jun 13 '18 at 05:42
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an example is to take a given real number in decimal notation and then split the notation to get two decimal representation. – Reza Habibi Jun 13 '18 at 05:44
@RezaHabibi You have to be a bit careful, though, since some reals have two different decimal representations. – Noah Schweber Jun 13 '18 at 16:00

Bijective function from $\Bbb R$ to $\Bbb R^2$

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