International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

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.

In this paper, the infinite numbers and functions are introduced and applied in modeling physical and mathematical systems and processes, where infinity somehow appears, i.e. infinite ladder electrical networks and systems instability analysis, series of numbers and limits calculation. Infinite numbers are defined as limits of complex functions that tend to infinity. Using these numbers it is possible to calculate the extended Laplace transform across the whole frequency spectrum as well as the extended bilateral Laplace transform, where the corresponding integral does not converge. Furthermore, the derivatives/integrals of the infinite number functions are determined. Using infinite numbers certain mathematical problems can be analysed and calculated, as well as problems in Physics and Engineering, where infinity appears, can be easily modeled and solved.