In the second half of the nineteenth century, the calculus was reformulated by Augustin-Louis Cauchy, Bernard Bolzano, Karl Weierstrass, Cantor, Dedekind, and others using the (ε, δ)-definition of limit and set theory.
•
Namely, such a null sequence becomes an infinitesimal in Cauchy's and Lazare Carnot's terminology.
Differential topology is the study of the (infinitesimal, local, and global) properties of structures on manifolds having no non-trivial local moduli, whereas differential geometry is the study of the (infinitesimal, local, and global) properties of structures on manifolds having non-trivial local moduli.
His most significant result is the research and of unitary and nonunitary dual group SU(n, 1), index generalization for semisimple Banach algebras, contributions to the research of Landau-type inequalities for infinitesimal generators to the theory of almost-summability.
Though the concepts of "continuity" and "infinitesimal" became important in mathematics during Newton and Leibniz's time (1680s), they were not well-defined until late 1810s.