## ABSTRACT

The determination of mathematical models is connected to the passage to the limit. The Cauchy principle is the practical method of proving of the convergence for the real numbers sequence. However, fundamental sequences may diverge for the incomplete spaces. These spaces can be extended by the completion technique. Then the fundamental sequence becomes convergent on completion. Besides, any element of the extended set can be obtained as a limit of the sequence of elements of the original set. The completion procedure, which is the basis of the sequential method, was tested on an incomplete space of rational numbers. Depending on the choice of the metric on this set, real or p-adic numbers were obtained.