  For any particularly interesting theorem one proof is never enough. Instead,
the first proof sets the challenge to find a more elegant method that
illuminates subtle features of the math, is simpler to understand, or even
avoids using controversial subjects. In this paper we consider a subject that
has attracted the attention of many mathematicians: the uncountability of the
real numbers in the unit interval. We present the most exhaustive collection of
proofs of this fact that we know. These range from Cantor's three published
proofs, including his famous diagonalization method, to more recent proofs that
employ measure theory, game theory, algebra, and analysis.
