mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word infinitesimal comes from a 17th-century...

generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus...

mathematics, the term infinitesimal generator may refer to: an element of the Lie algebra, associated to a Lie group Infinitesimal generator (stochastic...

In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the...

mathematics, an infinitesimal transformation is a limiting form of small transformation. For example one may talk about an infinitesimal rotation of a rigid...

from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions. The term is used in various...

or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using limits rather than infinitesimals. Nonstandard...

In mathematics, infinitesimal cohomology is a cohomology theory for algebraic varieties introduced by Grothendieck (1966). In characteristic 0 it is essentially...

The infinitesimal model, also known as the polygenic model, is a widely used statistical model in quantitative genetics and in genome-wide association...

Smooth infinitesimal analysis is a modern reformulation of the calculus in terms of infinitesimals. Based on the ideas of F. W. Lawvere and employing...

infinitesimal with respect to the other, is said to be Archimedean. A structure which has a pair of non-zero elements, one of which is infinitesimal with...

Leibniz, uses the symbols dx and dy to represent infinitely small (or infinitesimal) increments of x and y, respectively, just as Δx and Δy represent finite...

Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series...

nonstandard calculus is the modern application of infinitesimals, in the sense of nonstandard analysis, to infinitesimal calculus. It provides a rigorous justification...

Lie algebras (tangent vectors near the identity) may be thought of as infinitesimal symmetry motions. Thus Lie algebras and their representations are used...

In mathematics — specifically, in stochastic analysis — the infinitesimal generator of a Feller process (i.e. a continuous-time Markov process satisfying...

17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what...

An infinitesimal rotation matrix or differential rotation matrix is a matrix representing an infinitely small rotation. While a rotation matrix is an...

A pendulum is a body suspended from a fixed support such that it freely swings back and forth under the influence of gravity. When a pendulum is displaced...

Elementary Calculus: An Infinitesimal approach is a textbook by H. Jerome Keisler. The subtitle alludes to the infinitesimal numbers of the hyperreal number...

proper class containing not only the real numbers but also infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive...

In mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution P of a problem to slightly different solutions...

x_{0}} infinitely close to it, i.e. x − x 0 {\displaystyle x-x_{0}} is infinitesimal. As such, it is a mathematical implementation of the historical concept...

\textstyle \lim {\frac {\beta }{\alpha }}=1} , they are called equivalent infinitesimal (equiv. α ∼ β {\displaystyle \alpha \sim \beta } ). Moreover, if variables...

Calculus Made Easy is a book on infinitesimal calculus originally published in 1910 by Silvanus P. Thompson. The original text continues to be available...

In mathematics, the infinitesimal character of an irreducible representation ρ {\displaystyle \rho } of a semisimple Lie group G {\displaystyle G} on...

foundations were tacitly assumed to be definitive until the introduction of infinitesimal calculus by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century...

Nieuwentijdt's, in Lawvere's smooth infinitesimal analysis, characterized by the presence of nilsquare infinitesimals: "It may be said that Leibniz recognized...

mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is...

Cauchy continued to use infinitesimals in his own research as late as 1853. Cauchy gave an explicit definition of an infinitesimal in terms of a sequence...