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...

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

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...

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

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

extension of the real numbers to include certain classes of infinite and infinitesimal numbers. A hyperreal number x {\displaystyle x} is said to be finite...

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

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

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...

explicit use of indivisibles (indivisibles are geometric versions of infinitesimals). The work was originally thought to be lost, but in 1906 was rediscovered...

Evolution is the change in the heritable characteristics of biological populations over successive generations. It occurs when evolutionary processes such...

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

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

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

law for addition. Nevertheless, when dealing with infinitesimal rotations, second order infinitesimals can be discarded and in this case commutativity appears...

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

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

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

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...

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

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

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

transition-rate matrix (also known as a Q-matrix, intensity matrix, or infinitesimal generator matrix) is an array of numbers describing the instantaneous...

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...

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

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...

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

{df}{dx}}(a)} is as the ratio of an infinitesimal change in the output of the function f {\displaystyle f} to an infinitesimal change in its input. In order...

it appeared in print for the first time in his 1696 treatise on the infinitesimal calculus, entitled Analyse des Infiniment Petits pour l'Intelligence...