dual number
Language: English
Part of speech: noun
Forms: form: dual numbers
Senses: examples: text: This is particularly the case with regard to the pronouns of the dual number, which form one of the peculiarities of the language.
ref: 1840, George Grey, A Vocabulary of the Dialects of South Western Australia, 2nd edition, T. & W. Boone, page xi:
text: 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.
ref: 1998, William Blake Tyrrell, Larry J. Bennett, Recapturing Sophocles' Antigone, Rowman & Littlefield, page 43:
text: 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, […]
ref: 2006, Andrea Albrette, Teach Yourself Slovene, McGraw-Hill, page 19:
text: Classical Arabic has a fully functional dual number, which requires dual agreement in verbs, adjectives and pronouns.
ref: 2009, Giuliano Lancioni, “Formulaic models and formulaicity in Classical and Modern Standard Arabic”, in Roberta Corrigan, Edith A. Moravcsik, Hamid Ouali, Kathleen M. Wheatley, editors, Formulaic Language, Volume 1: Distribution and historical change, John Benjamins Publishing Company, page 225:
topics: grammar
human-sciences
linguistics
sciences
coordinate_terms: singular number
trial number
plural number
glosses: A grammatical number denoting a quantity of exactly two.
examples: text: 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.
text: In the special case of the algebra #92;mathbf#123;D#125; of dual numbers we get the vertical tangent bundle V.
ref: 1993, Ivan Kolář, Peter W. Michor, Jan Slovák, Natural Operations in Differential Geometry, Springer, page 336:
text: 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.
ref: 1996, Andrei N. Kolmogorov, Adolf-Andrei P. Yushkevich, translated by Roger Cooke, Mathematics of the 19th Century: Geometry, Analytic Function Theory, Birkhäuser, page 87:
text: 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.
ref: 2002, Jiří Tomáš, “Some Classification Problems on Natural Bundles Related to Weil Bundles”, in Olga Gil-Medrano, Vicente Miquel, editors, Differential Geometry, Valencia 2001: Proceedings of the International Conference, World Scientific, page 297:
topics: algebra
mathematics
sciences
hypernyms: hypercomplex number
glosses: 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.
Related terms: nilpotent