  Various versions of the definition of nonclassical symmetries existing in the
literature are analyzed. Comparing properties of Lie and nonclassical
symmetries leads to the conclusion that in fact a nonclassical symmetry is not
a symmetry in the usual sense. Hence the term "reduction operator" is suggested
instead of the name "operator of nonclassical symmetries". It is shown that in
contrast to the case of single partial differential equations a satisfactory
definition of nonclassical symmetries for systems of such equations has not
been proposed up to now. Moreover, the cardinality of essential nonclassical
symmetries is discussed, taking into account equivalence relations on the
entire set of nonclassical symmetries.
