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.
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