THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING
New concepts about the infinite numbers and functions and their application in modeling technological and mathematical problems
- ^{1} Applied Mathematics and Computers Laboratory (AMCL), Technical University of Crete, Chania, Crete, Greece
Abstract
In this paper more theory and examples about the infinite numbers and functions that were introduced in a previous paper is presented. These numbers and functions apply in modeling physical and mathematical systems and processes, where infinity somehow appears, i.e. series of numbers, limits calculation, kinematics problems, infinite expansion of certain universe geometric shapes. By strictly applying the theory of limits of functions, more properties of the infinite numbers which are limits of complex functions tending to infinity, are defined. The mirror infinite numbers and some properties of them are also demonstrated and presented. Furthermore, infinite geometric shapes whose sides are infinite numbers, as triangles, circles, spheres and ellipsoids are defined and used in modeling theoretical and technological problems.
Keywords
References
- E. Thalassinakis, “Infinite Numbers and Functions Applied in Modeling Technological Systems and in Solving Mathematical Problems in which Infinity Appears”, International Scientific Journal, Mathematical Modelling, ISSN (print) 2535-0986, ISSN (web) 2603-2929, Year VI, Issue 3/2022.
- T. Gowers, J. Barrow–Green, The Princeton Comparison to Mathematics, ISBN 978-0-691-11880-2, Princeton University Press, Feb 2010, pp. 20-490.
- J. W. Dauben, Georg Cantor: His Mathematics and Philosophy of the Infinite, Princeton University Press, Oct 1990, 1-424.
- A. Kanel-Belov, A. Chilikov, I. Ivanov-Pogodaev, S. Malev, E. Plotkin, J. T. Yu,; W. Zhang, “Nonstandard Analysis, Deformation Quantization and Some Logical Aspects of (Non) Commutative Algebraic Geometry”, Mathematics 2020, 8(10), 1694, https://doi.org/10.3390/math8101694 - 02, Oct 2020, 1-33.
- J. H. Keisler, Elementary Calculus: An Infinitesimal Approach, 3nd edition, Dover Publications, 2012, revised March 2021, 1-913.