Cardinality of $(0,1)^N$, where $(0,1)^N$ is set of sequences $\{x_i\}$, $x_i\in(0,1)$.

Question

I'm trying to prove, that if $(0,1)^N$ is a set of sequences $\{x_i\}$, $x_i\in(0,1)$, then $\#(0,1)^N$ is continuum. I would really appreciate any help with proving this in two ways: by finding bijection with $(0,1)$ and by using Cantor-Bernstein-Schröder Theorem.