  In this paper, we study the metric theory of dyadic approximation in the
middle-third Cantor set. This theory complements earlier work of Levesley,
Salp, and Velani (2007), who investigated the problem of approximation in the
Cantor set by triadic rationals. We find that the behaviour when we consider
dyadic approximation in the Cantor set is substantially different to
considering triadic approximation in the Cantor set. In some sense, this
difference in behaviour is a manifestation of Furstenberg's times 2 times 3
phenomenon from dynamical systems, which asserts that the base 2 and base 3
expansions of a number are not both structured.
