Show that the application $\Phi : \begin{aligned} \mathcal{P}(\mathbb{N}) &\rightarrow \{0,1\}^{\mathbb{N}} \\ A &\mapsto \mathbb{1}_A \end{aligned}$ is bijective.
Show that the application $\Phi : \begin{aligned} \mathcal{P}(\mathbb{N}) &\rightarrow \{0,1\}^{\mathbb{N}} \\ A &\mapsto \mathbb{1}_A \end{aligned}$ is bijective.