  The inversion of gravitational lens systems is hindered by the fact that
multiple mass distributions are often equally compatible with the observed
properties of the images. Besides using clear examples to illustrate the effect
of the so-called monopole and mass sheet degeneracies, this article introduces
the most general form of said mass sheet degeneracy. While the well known
version of this degeneracy rescales a single source plane, this generalization
allows any number of sources to be rescaled. Furthermore, it shows how it is
possible to rescale each of those sources with a different scale factor. Apart
from illustrating that the mass sheet degeneracy is not broken by the presence
of multiple sources at different redshifts, it will become apparent that the
newly constructed mass distribution necessarily alters the existing mass
density precisely at the locations of the images in the lens system, and that
this change in mass density is linked to the factors with which the sources
were rescaled. Combined with the fact that the monopole degeneracy introduces a
large amount of uncertainty about the density in between the images, this means
that both degeneracies are in fact closely related to substructure in the mass
distribution. An example simulated lensing situation based on an elliptical
version of a Navarro-Frenk-White profile explicitly shows that such
degeneracies are not easily broken by observational constraints, even when
multiple sources are present. Instead, the fact that each lens inversion method
makes certain assumptions, implicit or explicit, about the smoothness of the
mass distribution means that in practice the degeneracies are broken in an
artificial manner rather than by observed properties of the lens system.
