# dual

Pronunciation: US say "DOO-uhl" /ˈdu.əl/; UK say "DYOO-uhl" /ˈdjuː.əl/

## Adjective

1. Made up of two components that are usually equivalent to each other.
   - Simple: Having two parts that are usually equal or matching.
   - _The aircraft was fitted with a dual hydraulic system for safety._
   - _Their new phone runs on a dual battery design._
2. Relating to two, or to a pair of things.
   - Simple: Relating to two things or to a pair.
   - _They signed a treaty serving the dual interests of both nations._
   - _The committee debated the dual aims of the new policy._
3. Relating to a grammatical number found in certain languages that marks exactly two of something, distinct from singular and plural.
   - Simple: In some languages, used for a special word form that means exactly two of something.
   - _Slovene grammar attaches dual forms to nouns referring to two items._
   - _Several ancient languages used a dual ending for naturally paired body parts._
5. Showing duality, where one structure corresponds to another in a paired and often reversible way.
   - Simple: Having two forms that match each other in a balanced, mirror-like way.
   - _Wave-particle behavior is a dual phenomenon at the heart of quantum mechanics._
   - _The two formulations turned out to be dual descriptions of the same physics._
9. Describing the space consisting of all linear functionals defined on another given vector space.
   - Simple: In math, describing a space made from all the linear functions of another space.
   - _The dual space collects every linear functional acting on the original vectors._
   - _For a finite-dimensional vector space, the dual space has the same dimension._
12. Describing a category that contains the same objects as another but has the direction of every morphism reversed.
   - Simple: In math, describing a category with the same objects but with all its arrows pointing the opposite way.
   - _Working in the dual category lets one read off a second result for free._
   - _Many theorems come in pairs, with one holding in the dual category._

## Noun

4. In certain languages, the grammatical number used for exactly two of something, as distinct from the singular and the plural.
   - Simple: In grammar, the special word form used when talking about exactly two of something.
   - _Classical Arabic preserves a dual that nouns, verbs, and pronouns all inflect for._
   - _In Old English, the dual survived only in a couple of pronoun forms._
6. The other member of a pair, considered in relation to the one you already have.
   - Simple: The matching second thing in a pair, when you already have one of them.
   - _If this glove is the left one, then its dual is the right._
   - _She matched each earring with its dual before packing them away._
7. A meet or match in which two teams compete directly against each other, for example two high schools or two colleges.
   - Simple: A sports contest between just two teams, often two schools.
   - _The track team edged out a narrow win in last weekend's dual._
   - _Both colleges treated the annual dual as the highlight of the season._
10. For a vector in an inner product space, the linear functional that corresponds to taking the inner product with that same vector.
   - Simple: In math, the linear function tied to a vector that takes its inner product with other vectors.
   - _Each vector has a dual that acts on the space through the inner product._
   - _We computed the dual of the basis vector and checked the result._
11. For a regular polyhedron, the polyhedron obtained by swapping the roles of vertices and faces, so that faces become corners and corners become faces.
   - Simple: In geometry, the matching shape made by swapping the corners and faces of a solid shape.
   - _Builders of geometric models often pair a solid with its dual._
   - _The dual of the icosahedron is the dodecahedron._

## Verb

8. To convert something from single to dual form, especially to upgrade a single-carriageway road into a dual carriageway.
   - Simple: To rebuild a single road so it has two separated lanes for each direction.
   - _The county finally agreed to dual the dangerous mountain road._
   - _Engineers dualed the aging two-lane route last summer._

## Origin

Borrowed from Latin dualis ("two"), formed from duo ("two") plus the adjective suffix -alis.

Source: DictionaryAI, https://dictionaryai.com/define/dual (written from Wiktionary data, CC BY-SA 4.0: https://creativecommons.org/licenses/by-sa/4.0/).