  Current-voltage measurements in electrical impedance tomography can be
partially ordered with respect to definiteness of the associated self-adjoint
Neumann-to-Dirichlet operators (NtD). With this ordering, a point-wise larger
conductivity leads to smaller current-voltage measurements, and smaller
conductivities lead to larger measurements.
  We present a converse of this simple monotonicity relation and use it to
solve the shape reconstruction (aka inclusion detection) problem in EIT. The
outer shape of a region where the conductivity differs from a known background
conductivity can be found by simply comparing the measurements to that of
smaller or larger test regions.
