  It has been argued by several authors that the quantum mechanical spectrum of
black hole horizon area must be discrete. This has been confirmed in different
formalisms, using different approaches. Here we concentrate on two approaches,
the one involving quantization on a reduced phase space of collective
coordinates of a Black Hole and the algebraic approach of Bekenstein. We show
that for non-rotating, neutral black holes in any spacetime dimension, the
approaches are equivalent. We introduce a primary set of operators sufficient
for expressing the dynamical variables of both, thus mapping the observables in
the two formalisms onto each other. The mapping predicts a Planck size remnant
for the black hole.
