A task given to us is about proving that the interval $X=[0,1]$ and the square $Y=[0,1] × [0,1]$ are equipotent.
Part 1 asks to find an injective function $f : X \rightarrow Y$
Part 2 asks to find an injective function $g : Y \rightarrow X$
I can't seem to find the answer to these two and I imagine they are more obvious than what it seems. I know that the Cantor-Bernstein-Schröder theorem has to be used eventually. Any help would be greatly appreciated.