@ZachWeiner@steuard This type of machine can't exist, but its non-existence depends only on logic, not physics, so it would be independent of the laws of physics under which we live.
@ZachWeiner@steuard Maybe something forbidden by logic but not necessarily physics, for example a machine which could understand and answer any question truthfully (it would also know if it has a truth value at all), I think this would contradict the decision problem.
@ZachWeiner I guess all objects would be Gabriel's horns (if by that you mean finite volume and infinite surface) if you assume you can measure arbitrarily small things, I don't think that's the case when taking quantom mechanics into account though.
@AcademicsSay It doesn't specify you choose one at random from the 4 presented, so it could be any real number, and the probability of choosing a specific number at random from the real set is 0.