dual

Etymology

PIE word *dwóh₁ Borrowed from Latin dualis (“two”), from duo (“two”) + adjective suffix -alis.

adj

1. Characterized by having two (usually equivalent) components.
   a dual-motor vehicle
2. Pertaining to two, pertaining to a pair of.
   dual engine failure
   dual citizenship
   Both Deborah and Samuel held dual roles as judges and prophets. 2020, Grace Ying May, “Women Disciplining Men: A Biblical Pattern of Leadership”, in Aída Besançon Spencer, William David Spencer, editors, Christian Egalitarian Leadership: Empowering the Whole Church According to the Scriptures, page 48
3. (grammar) Pertaining to a grammatical number in certain languages that refers to two of something, such as a pair of shoes.
   Modern Arabic displays a dual number, as did Homeric Greek.
4. (mathematics, physics) Exhibiting duality.
5. (linear algebra) Being the space of all linear functionals of (some other space).
   Accordingly, a hyperplane in the sample space is dual to a subspace in the variable space. 2012, Doug Fisher, Hans-J. Lenz, Learning from Data: Artificial Intelligence and Statistics V, Springer Science & Business Media, page 81
6. (category theory) Being the dual of some other category; containing the same objects but with source and target reversed for all morphisms.
   Every category is dual to its own dual, so if a statement holds in all categories so does its dual. 1992, Colin McLarty, Elementary Categories, Elementary Toposes, Clarendon Press, page 77

noun

1. Of an item that is one of a pair, the other item in the pair.
2. (geometry) Of a regular polyhedron with V vertices and F faces, the regular polyhedron having F vertices and V faces.
   The octahedron is the dual of the cube.
3. (grammar) The dual number.
4. (mathematics) Of a vector in an inner product space, the linear functional corresponding to taking the inner product with that vector. The set of all duals is a vector space called the dual space.

verb

1. (transitive) To convert from single to dual; specifically, to convert a single-carriageway road to a dual carriageway.
   I have to declare an interest and I do so with some ambivalence because if the road is dualled it is likely to take half of my front garden. 1994, Great Britain. Parliament. House of Commons, Parliamentary Debates
   The power generation and propulsion systems are dualled to accommodate component failure and maintain propulsion at reduced speed should any part of one system be lost. 2006, David Lowe, Intermodal Freight Transport, page 163
   The investment will allow Nexus to increase service frequencies, reduce journey times, and improve reliability by dualling three sections of line between Pelaw and South Shields. September 22 2021, “Network News: Nexus increases Tyne and Wear Metro train order to 46”, in RAIL, number 940, page 23