Show that the set of all infinite sequences of natural numbers \(\mathbb{N}^{\mathbb{N}}\) has cardinality \(\mathfrak{c}\). [use that \(\#\{0,1\}^{\mathbb{N}}=\#\{1,2\}^{\mathbb{N}},\{1,2\}^{\mathbb{N}} \subset \mathbb{N}^{\mathbb{N}} \subset \mathbb{R}^{\mathbb{N}}\) and \(\# \mathbb{R}^{\mathbb{N}}=\#(0,1)^{\mathbb{N}}\).]