Calculus of Infinitesimals and Ultra Real Numbers

Exploring Infinitesimals and Ultra Real Numbers in Calculus

Abstract

Leibnitz proposed infinitely small differentiable i.e., infinitesimal of the first and second orders. He regarded his theory of infinitesimal as foundation for the theory of limits. eohen argued the existence of infinitesimal as the reciprocals of transfinite number. Archimedian property for real numbers system R, existence of infinitely small magnitude (infinitesimal) in comparison with other real number is not possible.The case of Horn angle is the angle between a curve and its tangent which intersect at origin the proper measurement of horn angle we have to measure beyond the domain of real numbers. The magnitude of the angle C_1 OC_2 may be called ultra-real numbers.