  We argue that the widely spread opinion that the left-handed media (LHM) are
characterized by a negative refractive index $n_-$ is misleading.
  Since n does not enter into Maxwell's equations and boundary conditions, any
medium may be described by both positive n and negative $n_-=-n$. Two
thermodynamic inequalities are presented, that make a difference between the
LHM and the regular media (RM). The first one reads that the group velocity is
positive in the RM and negative in the LHM. The second one is that the product
${\rm Re}(n) {\rm Im}(n)$ is positive in the RM and negative in the LHM. Both
inequalities are invariant with respect to the change $n \to n_-$. However, to
use $n_-$ one should change some traditional electrodynamics definitions.
