# Proving equinumerosity form unit circle to [0,1]

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.