I need to prove equinumerosity of the following using the Schröder–Bernstein theorem:

$[0, 1] ∼\{(x, y) ∈ R^2 | x^2 + y^2 = 1\}$

And I'm having some trouble with finding an injective function $\Leftarrow$ and could use some help.

Thanks in advance.


Use the angle in polar coordinates.


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