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4 Yaroslav D. Sergeyevto work with sets having measure zero as with normal sets;to calculate lengths, areas, and volumes of fractals at infinity;to define and calculate volumes of objects having parts of different dimensions in aunique framework;to elaborate new mathematical models working simultaneously at micro and macro levelsin a unique framework.References[1] Ya.D. Sergeyev, Arithmetic of infinity, Edizioni Orizzonti Meridionali, CS, 2003.[2] Ya.D. Sergeyev, Computer system for storing infinite, infinitesimal, and finite quantities and executing arithmeticaloperations with them, Patent filed in 2004.[3] Ya.D. Sergeyev, Infinity computer and calculus, Opening plenary lecture at the congress SInfinity in Mathematics,Physics, and Philosophy T, Pisa, Italy, 2004.[4] Ya.D. Sergeyev, A new computational paradigm, Invited plenary lecture at the VI-th International Congresson Mathematical Modelling, Nizhni Novgorod, Russia, 2004.[5] Ya.D. Sergeyev, Infinity computer and calculus, Invited plenary lecture, International Conference SNumericalAnalysis: the State of the Art T, 2005.[6] Ya.D. Sergeyev, Infinity computer and calculus, Invited plenary lecture, International Conference on DifferenceEquations, Special Functions and Applications, 2005.