  To make research of chaos more friendly with discrete equations, we introduce
the concept of an unpredictable sequence as a specific unpredictable function
on the set of integers. It is convenient to be verified as a solution of a
discrete equation. This is rigorously proved in this paper for quasilinear
systems, and we demonstrate the result numerically for linear systems in the
critical case with respect to the stability of the origin. The completed
research contributes to the theory of chaos as well as to the theory of
discrete equations, considering unpredictable solutions.
