Let \(\left(A_{i}ight)_{i \in \mathbb{N}}\) be a sequence of sets of cardinality (\mathfrak{c}\). Show that \(\# \bigcup_{i \in \mathbb{N}} A_{i}=\mathfrak{c}\).
[map \(A_{i}\) bijectively onto \((i-1, i)\) and use that \((0,1) \subset \bigcup_{i=1}^{\infty}(i-1, i) \subset \mathbb{R}\).]