ABSTRACT
In this chapter, we consider the relationships between the objects under study, namely, between differential and difference equations and transformation groups admitted by them.
Using the Taylor series, one can readily write out the differential representation of a given difference equation. This is a formal power series whose sum truncated at a certain term is the so-called differential approximation to the difference equation. The differential representation (an infinite-order differential equation) formally admits the same transformation group as the original difference equation, but the differential approximation, which is a finite-order differential equation, may preserve the symmetry of neither the original equation nor the difference equation.
