dual number

Noun

dual number (plural dual numbers)

1. A grammatical number denoting a quantity of exactly two.
   • This is particularly the case with regard to the pronouns of the dual number, which form one of the peculiarities of the language.1840, George Grey, A Vocabulary of the Dialects of South Western Australia, 2nd edition, T. & W. Boone, page xi
   • 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...1998, William Blake Tyrrell, Larry J. Bennett, Recapturing Sophocles' Antigone, Rowman & Littlefield, page 43
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.
   • 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...
   • In the special case of the algebra #92;mathbf#123;D#125; of dual numbers we get the vertical tangent bundle V.1993, Ivan Kolář, Peter W. Michor, Jan Slovák, Natural Operations in Differential Geometry, Springer, page 336