Methods of Numeration of Discrete Sequences

Introduction. Numeration, or code, discrete sequences act fundamental part in the theory of recognition and estimation. By code get codes indexes programs calculated functions. It is set that universal are which will realize all other programs. This one basic results On basis numeration Godel proved a famous theorem about incompleteness arithmetic. Purpose article. To develop synonymous numerations by natural numbers eventual calculable functions mutually. Results. built for four commands machine with unlimited registers (MUR) type 4u, 4u +1, 4u+2, 4u+3 accordingly. Every program consists complete list commands. bijection MUR certainly mutually MUR. Thus, on it possible effectively to find its number, vice versa, number program. Conclusions. Synonymous developed mutually, Leaning against functions, are, application s-m-n got operation functions: combination φx φy, giving work φxφy, conversion effective recursion. index function φxφy x y [2]. Keywords: numeration, diagonal method.