The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable? How can I prove that the set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?
Edit:  This answer came to mind.  Is it correct?
This answer just came to mind.  By contradiction suppose the set is $\{f_n\}_{n \in \mathbb{N}}$.  Define the function $f: \mathbb{N} \to \{0,1\}$ by $f(n) \ne f_n(n)$.  Then $f \notin\{f_n\}_{n \in \mathbb{N}}$.

Hint : use the diadic developpement of elements of $[0,1]$.
