elementary set theory - How do I create an injection here?

I am trying to show that $|\Bbb {R} \times \Bbb {R}| \leq |\Bbb {R}|$.

I don't know how to define $f:\Bbb {R} \times\Bbb {R} \rightarrow \Bbb {R}$ in a way that would make $f$ injective.

My professor gave us the hint that $(0,1) \sim \Bbb {R}$ would imply that $|(0,1) \times (0,1)| \leq |(0,1)|$, but I don't understand how that is helpful here.