If \(A \subset \mathbb{N}\) we can identify the indicator function \(\mathbb{1}_{A}: \mathbb{N} ightarrow\{0,1\}\) with the 0 -1-sequence \(\left(\mathbb{1}_{A}(i)ight)_{i \in \mathbb{N}}\), i.e. \(\mathbb{1}_{A} \in\{0,1\}^{\mathbb{N}}\). Show that the map \(\mathscr{P}(\mathbb{N}) i A \mapsto \mathbb{1}_{A} \in\{0,1\}^{\mathbb{N}}\) is a bijection and conclude that \(\# \mathscr{P}(\mathbb{N})=\mathfrak{c}\).