Definition, Meaning & Synonyms | English word INFINITESIMAL

---

Definitions of INFINITESIMAL

1. Incalculably, exceedingly, or immeasurably minute; vanishingly small.
2. (mathematics) Of or pertaining to values that approach zero as a limit.
3. (informal) Very small.
4. (mathematics) A non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number).

---

---

---

---

---

---

---

---

---

Examples of Using INFINITESIMAL in a Sentence

• Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.
• In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space.
• Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for formulating infinitesimal calculus, though he developed calculus years before Leibniz.
• The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers.
• This definition of surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.
• A spinor transforms linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation, but unlike geometric vectors and tensors, a spinor transforms to its negative when the.
• The electric field is defined as a vector field that associates to each point in space the force per unit of charge exerted on an infinitesimal test charge at rest at that point.
• Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics.
• In mathematics, the surreal number system is a totally ordered proper class containing not only the real numbers but also infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number.
• The definitions of multiplicities that was given during the first half of the 20th century involved continuous and infinitesimal deformations.
• Infinitesimals do not exist in the standard real number system, but they do exist in other number systems, such as the surreal number system and the hyperreal number system, which can be thought of as the real numbers augmented with both infinitesimal and infinite quantities; the augmentations are the reciprocals of one another.
• In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness) at each point of space can be assumed to be unchanged by the deformation.
• Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).
• Roberval was one of those mathematicians who, just before the invention of the infinitesimal calculus, occupied their attention with problems which are only soluble, or can be most easily solved, by some method involving limits or infinitesimals, which would today be solved by calculus.
• Johann Bernoulli (1667–1748; also known as Jean), mathematician and early adopter of infinitesimal calculus.
• A differential -form can be thought of as measuring an infinitesimal oriented area, or 2-dimensional oriented density.
• More generally, the technique of microadditivity (which can used to derive theorems in physics) makes use of nilpotent or nilsquare infinitesimals and is part smooth infinitesimal analysis.
• Instead, analysts were often forced to invoke infinitesimal, or "infinitely small", quantities to justify their algebraic manipulations.
• An algebraic structure in which any two non-zero elements are comparable, in the sense that neither of them is infinitesimal with respect to the other, is said to be Archimedean.
• He is known for his contributions to infinitesimal calculus and educating Leonhard Euler in the pupil's youth.
• Fermions transforming as 1 under SU(5) are now thought to be necessary because of the evidence for neutrino oscillations, unless a way is found to introduce an infinitesimal Majorana coupling for the left-handed neutrinos.
• The fundamental "linearizing" assumptions of linear elasticity are: infinitesimal strains or "small" deformations (or strains) and linear relationships between the components of stress and strain.
• To form a relationship between the voltage and current measured on the one hand, and the material's resistivity on the other, it is necessary to apply the distributed-element model by considering the material to be an array of infinitesimal resistor elements.
• Lie algebroids play a similar same role in the theory of Lie groupoids that Lie algebras play in the theory of Lie groups: reducing global problems to infinitesimal ones.
• In Einstein notation for tensors, with summation over repeated indices, for unit volume, the infinitesimal statement is.

Page preparation took: 390.12 ms.