  We give a simple example of a set that is weakly Dedekind infinite (= can be
mapped onto omega) but dually Dedekind finite (=cannot be mapped noninjectively
onto itself), namely, the power set of a superamorphous set. (A infinite set is
superamorphous if all finitary relations on it are definable in the language of
equality.)
  We also show that the property of "inexhaustibility" is not closed under
supersets unless the full axiom of choice holds.
