ABSTRACT
This chapter considers the general definition of the convergence. The sequence tends to a limit if its elements with large enough numbers are close enough to this limit. The reliable method of analysis of the convergence for non-complete spaces is based on the technique of Georg Cantor's definition of real numbers. The space of rational numbers is non-complete. However, each non-convergent fundamental sequence of rational numbers determines an irrational real number. A fundamental sequence of the arbitrary metric space can be non-convergent. However, it has a limit on the extension of the given space, which is called its completion. The determined sequential state is the analogue of the Cantor real number, the p-adic number, the sequential control, and the element of the completion of a metric space. The existence of a certain connection between the sequential and generalized models is indicated by the fact that in both cases the state of the system is associated with the same Sobolev space.
