dual number

English

Noun

dualnumber(pluraldual numbers)

1. (grammar)A grammaticalnumberdenoting a quantity of exactly two.

   Coordinate terms:singularnumber,trialnumber,pluralnumber

   • 1840,George Grey,A Vocabulary of the Dialects of South Western Australia,2nd edition, T. & W. Boone,page xi:

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

   • 1998,William Blake Tyrrell, Larry J. Bennett,Recapturing Sophocles' Antigone,Rowman & Littlefield,page43:

     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.¹By uniting them with thedual numberin the description of their deaths, Sophocles has the elders speak of them as indistinguishable in their hatred, spear work, and deaths.

   • 2006,Andrea Albrette,Teach Yourself Slovene,McGraw-Hill,page19:

     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. Thisdual numberexisted in many languages at one stage in their development, but has been lost; in Slovene, though,[…]

   • 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,page225:

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

2. (algebra)An element of analgebra(thealgebra of dual numbers) which includes thereal numbersand an element ε which satisfies ε ≠ 0 and ε² = 0.

   Hypernym:hypercomplex number

   Iff(x) is a polynomial or a power series then its derivative can be obtained “automatically” usingdual numbersas follows:$f'(x)={f(x+\epsilon )-f(x) \over \epsilon }$where$f(x+\epsilon )$should be expanded using the algebra ofdual numbers.The role of theεis therein similar to that of an infinitesimal.

   • 1993,Ivan Kolář, Peter W. Michor, Jan Slovák,Natural Operations in Differential Geometry,Springer,page336:

     In the special case of the algebra$\mathbf {D}$ofdual numberswe get the vertical tangent bundle$V$.

   • 1996,Andrei N. Kolmogorov, Adolf-Andrei P. Yushkevich, translated by Roger Cooke,Mathematics of the 19th Century: Geometry, Analytic Function Theory,Birkhäuser,page87:

     These numbers are now calleddual numbers(a term due toStudy) and can be defined as expressions of the form$a+b\epsilon$,$\epsilon ^{2}=0$.When this is done asKotel'nikovand Study showed, the dual distance between two points of this sphere representing two lines, forming an angle$\varphi$and having shortest distance$d$,is equal to thedual number$\varphi +\epsilon d$,while the motions of Euclidean space are represented by rotations of the dual sphere, and consequently depend on three dual parameters.

   • 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,page297:

     Thus we investigate natural$T$-functions defined on$T^{*}T^{\mathbf {D} \otimes A}M$to determine all natural operators$T\to TT^{*}T^{A}$for$\mathbf {D}$denoting the algebra ofdual numbers.

Translations

grammatical number denoting a quantity of exactly two—seedual

element of the algebra of dual numbers

• Polish:liczba dualnaf

The translations below need to be checked and inserted above into the appropriate translation tables. See instructions atWiktionary:Entry layout § Translations.

Translations to be checked

• Welsh:^{(pleaseverify)}rhif deuolm

See also

• nilpotent

Further reading

• Dual (grammatical number)on Wikipedia.Wikipedia
• Dual numberon Wikipedia.Wikipedia