Applied Physics and Mathematics Annotation << Back CLASSICAL CONTINUITY AND ITS DISCRETE VARIANT V.K. LEONTIEV, E.N. GOPRDEEV, M.-S.А. VOLKOV The paper considers various issues concerning the discrete variant of the approach to the concept of “continuity”. The concept of continuity in classical mathematics is one of the basic and well-studied for a long time. The theory of continuous and discontinuous functions was well studied more than a century ago. In discrete mathematics, an attempt to introduce the concept of “continuity” was made by V.K.Leontiev in 2015 when considering diophantine equations and in connection with Boolean optimization problems. In applied mathematics, Boolean optimization and Diophantine equations are urgent problems, especially in connection with the development of cryptographic methods of information protection. This paper is devoted to the discussion of continuous linear forms. The relation of the latter to the concept of classical continuity. The arguments in favor of the relevance of the use of the introduced concepts are given. In addition, some results have been obtained that are of interest for solving discrete optimization problems. Keywords: continuous function, Baer classes, Boolean equations, Boolean programming problem, linear transformation, continuous linear form. DOI: 10.25791/pfim.01.2022.1221 Pp. 31-37.