Meaning of dual number | Babel Free

Definitions

1. A grammatical number denoting a quantity of exactly two.
2. An element of an algebra (the algebra of dual numbers) which includes the real numbers and an element ε which satisfies ε ≠ 0 and ε² = 0.

Examples

“This is particularly the case with regard to the pronouns of the dual number, which form one of the peculiarities of the language.”

“Eteocles and Polyneices are enemy brothers, that is, they are alike in spite of the difference erected by being on opposite sides of the Theban battlements.¹ By uniting them with the dual number in the description of their deaths, Sophocles has the elders speak of them as indistinguishable in their hatred, spear work, and deaths.”

“In most languages, singular and plural are used to indicate number. Slovene, however, has an additional ‘dual’ number, which is used when referring to two of anything. This dual number existed in many languages at one stage in their development, but has been lost; in Slovene, though, […]”

“Classical Arabic has a fully functional dual number, which requires dual agreement in verbs, adjectives and pronouns.”

“If f(x) is a polynomial or a power series then its derivative can be obtained “automatically” using dual numbers as follows: f'(x)#61;#123;f(x#43;#92;epsilon)-f(x)#92;over#92;epsilon#125; where f(x#43;#92;epsilon) should be expanded using the algebra of dual numbers. The role of the ε is therein similar to that of an infinitesimal.”

“In the special case of the algebra #92;mathbf#123;D#125; of dual numbers we get the vertical tangent bundle V.”

“These numbers are now called dual numbers (a term due to Study) and can be defined as expressions of the form a#43;b#92;epsilon, #92;epsilon²#61;0. When this is done as Kotel'nikov and Study showed, the dual distance between two points of this sphere representing two lines, forming an angle #92;varphi and having shortest distance d, is equal to the dual number #92;varphi#43;#92;epsilond, while the motions of Euclidean space are represented by rotations of the dual sphere, and consequently depend on three dual parameters.”

“Thus we investigate natural T-functions defined on T#42;T#123;#92;mathbf#123;D#125;#92;otimesA#125;M to determine all natural operators T#92;toTT#42;Tᴬ for #92;mathbf#123;D#125; denoting the algebra of dual numbers.”

CEFR level