  Recently, [{arXiv:0810.3134}] is accepted and published. We present ultimate
version of no-hidden-variables theorem. We derive a proposition concerning the
quantum theory under the existence of the Bloch sphere in a single spin-1/2
system. The existence of a single classical probability space for measurement
outcome within the formalism of von Neumann's projective measurement does not
coexist with the proposition concerning the quantum theory. We have to give up
the existence of such a classical probability space for measurement outcome in
the two-dimensional Hilbert space formalism of the quantum theory. The quantum
theory does not accept a hidden-variable interpretation in the two-dimensional
space.
