  Expansion of real numbers is a basic research topic in number theory. Usually
we expand real numbers in one given base. In this paper, we begin to
systematically study expansions in multiple given bases in a reasonable way,
which is a generalization in the sense that if all the bases are taken to be
the same, we return to the classical expansions in one base. In particular, we
focus on greedy, quasi-greedy, lazy, quasi-lazy and unique expansions in
multiple bases.
