  While one can in principle augment gravity theory with torsion, it is
generally thought that any such torsion affects would be too small to be of
consequence. Here we show that this cannot in general be the case. We show that
the limit of vanishing torsion is not necessarily a continuous one, with the
theory obtained in the limit not necessarily coinciding with the theory in
which torsion had never been present at all. However, for a standard torsion
tensor that is antisymmetric in two of its indices we have found two cases in
which the vanishing torsion limit is in fact continuous, namely Einstein
gravity and conformal gravity. For other gravity theories of common interest to
possess a continuous limit the torsion tensor would need to be antisymmetric in
all three of its indices.
