Calculus of Infinitesimals and Ultra Real Numbers
Exploring Infinitesimals and Ultra Real Numbers in Calculus
by Dr. Vijay Kumar*,
- Published in Journal of Advances and Scholarly Researches in Allied Education, E-ISSN: 2230-7540
Volume 16, Issue No. 4, Mar 2019, Pages 1519 - 1521 (3)
Published by: Ignited Minds Journals
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.
KEYWORD
Calculus, Infinitesimals, Ultra Real Numbers, Leibnitz, Infinitesimal, Theory of limits, Transfinite number, Archimedian property, Magnitude, Horn angle
