LIMITED INFINITY

Abstract

The paper discusses the identification of the concept of limited infinity, highlighting its relevance in expanding the range of mathematical tools necessary for solving complex applied design tasks in technics. Limited infinity extends the applicability of classical infinity in mathematical problems. The primary objective of the paper is to develop the concept of limited infinity and conduct comprehensive research on it. The paper outlines the fundamental properties of limited infinity, elucidating its key characteristics and practical applications. An analysis of basic mathematical operations involving limited infinity demonstrates that, under certain conditions, it behaves similarly to a finite number. Furthermore, a comparative analysis of infinity, limited infinity, and sets clarifies the concept of limited infinity. To facilitate comparisons involving values represented with limited infinity, the paper proposes several comparative estimates: the absolute integral estimate, the relative average integral estimate, and the number of grid nodes of permissible errors. Additionally, the paper provides examples illustrating the application of limited infinity in practical problems such as using the quasi-constant and functional convergence methods. The introduction of the concept of limited infinity notably streamlines the utilization of various forms of infinity in applied tasks, especially when solving systems of equations with undetermined solutions.