# Vocabulary Word

**Word:**infinitesimal

**Definition:**very small

## Sentences Containing 'infinitesimal'

A "connection" on a G bundle tells you how to glue F's together at nearby points of M. It starts with a continuous symmetry group G which acts on the fiber F, and then it associates a group element with each infinitesimal path.

Dirac's monopole solution in fact describes an infinitesimal line solenoid ending at a point, and the location of the solenoid is the singular part of the solution, the Dirac string.

For infinitesimal paths, the group element is 1 + "iA""μ""dx""μ" which implies that for finite paths parametrized by "s", the group element is:
The map from paths to group elements is called the Wilson loop or the holonomy, and for a U(1) gauge group it is the phase factor which the wavefunction of a charged particle acquires as it traverses the path.

For infinitesimal paths, the group element is close to the identity, while for longer paths the group element is the successive product of the infinitesimal group elements along the way.

In mathematics, tiny and miny are operators that yield infinitesimal values when applied to numbers in combinatorial game theory.

On this head, Mr. Mivart remarks, "As, according to Mr. Darwin's theory, there is a constant tendency to indefinite variation, and as the minute incipient variations will be in ALL DIRECTIONS, they must tend to neutralize each other, and at first to form such unstable modifications that it is difficult, if not impossible, to see how such indefinite oscillations of infinitesimal beginnings can ever build up a sufficiently appreciable resemblance to a leaf, bamboo, or other object, for natural selection to seize upon and perpetuate."

Roughly speaking, Deligne–Mumford stacks can be thought of as algebraic stacks whose objects have no infinitesimal automorphisms.

Specifically, though ⧾G is infinitesimal with respect to ↑ for all positive values of "x", ⧾⧾⧾G is equal to up.

The constant ("a") is the number of individuals that share a unit of habitat at infinitesimal density and may be 0.

The operator "A" is said to be the infinitesimal generator of the semigroup.

The physician, with his invaluable microscope, counts the number of infinitesimal corpuscles in the blood and bases his prescription on that count; he examines the sputum of a patient to determine whether tuberculosis wastes the system.

The wave functions have a direct interpretation as a probability distribution:
gives the probability of finding the particle in an infinitesimal interval of length formula_52 about some point formula_53.

This criterion is the largest acceptable spot size diameter that an infinitesimal point is allowed to spread out to on the imaging medium (film, digital sensor, etc.).

With respect to the former, he says: "The explanation of their ORIGIN is deemed thoroughly unsatisfactory--utterly insufficient to explain the incipient, infinitesimal beginnings of structures which are of utility only when they are considerably developed."

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