dual

Pluralduals

Formsduals

1. 1
   adjective

   Made up of two components that are usually equivalent to each other.

   The aircraft was fitted with a dual hydraulic system for safety.

   Their new phone runs on a dual battery design.

   Similardouble, twin

   Oppositesingle

   Note

   Latin supplied the word ready-made: dualis, from duo, "two", plus the adjective ending -alis. Every sense of the word grows from that root. Here the two parts belong to a single thing, and the word often joins a noun in hyphenated compounds such as a dual-motor vehicle. It does not take degrees: something is dual or it is not, and nothing is more dual than something else.

2. 2
   adjective

   Relating to two, or to a pair of things.

   They signed a treaty serving the dual interests of both nations.

   The committee debated the dual aims of the new policy.

   Similardouble, duplicate, twofold

   Oppositesingle

   Note

   The looser, relational use describes two things held or done at once rather than two parts built into one object. It settles into fixed pairings such as dual roles, dual engine failure and above all dual citizenship. That last phrase carries legal weight: in 2021 Jessie Yeung reported that a Japanese court had upheld the country's ban on it. Double often fits the same slot, while duplicate suggests a copy, which dual does not.

3. 3
   adjective

   Relating to a grammatical number found in certain languages that marks exactly two of something, distinct from singular and plural.

   Slovene grammar attaches dual forms to nouns referring to two items.

   Several ancient languages used a dual ending for naturally paired body parts.

   Note

   A grammarian's term, applied to the number itself and to the forms that mark it: a dual number, dual forms, a dual ending. The category is one that languages keep or lose over time. Modern Arabic still has it, Homeric Greek had it, and Sanskrit shows it as well. Whenever the category is named as a thing rather than described, the word becomes the noun in grammar.

4. 4
   nouncountable

   In certain languages, the grammatical number used for exactly two of something, as distinct from the singular and the plural.

   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.

   Note

   Grammarians clip dual number to the dual, just as they say the singular and the plural, and a form is said to be in the dual. A full paradigm then reads singular, dual, plural. The languages that keep the category belong with the adjective in grammar. The noun is simply the handier tool for naming it.

5. 5
   adjective

   Showing duality, where one structure corresponds to another in a paired and often reversible 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.

   Note

   The umbrella sense, which the more exact mathematical uses narrow down. Two structures are dual when a correspondence carries one onto the other with roles systematically swapped, such as points and lines in geometry or strong and weak coupling in physics. The relationship runs both ways, and that is what separates dual from merely paired: each side can be read as the other's mirror image.

6. 6
   nouncountable

   The other member of a pair, considered in relation to the one you already have.

   If this glove is the left one, then its dual is the right.

   She matched each earring with its dual before packing them away.

   Similarcounterpart, partner, mate, match

7. 7
   nouncountable

   A meet or match in which two teams compete directly against each other, for example two high schools or two colleges.

   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.

   Similarmeet

   Note

   A wrestling word for team against team, as opposed to a meet with many schools. It takes the plural freely: Kevin Revolinski's Insiders' Guide to Madison lists wrestling duals and meets side by side. It often carries a proper name, as in the Ter-Hark Cup wrestling dual. Mark Schultz's Foxcatcher stretches it to an international team match, the Bulgarian dual.

8. 8
   verbtransitive

   To convert something from single to dual form, especially to upgrade a single-carriageway road into a dual carriageway.

   The county finally agreed to dual the dangerous mountain road.

   Engineers dualed the aging two-lane route last summer.

   Note

   The verb's spelling divides: dualled and dualling in UK spelling, dualed and dualing in US spelling. Its home is roads, as when the House of Commons heard in 1994 of a road to be dualled. Tyne and Wear's Nexus applies it to dualling sections of rail line. Engineers stretch it further still, to power and propulsion systems that are dualled so that one can fail without stopping the whole.

9. 9
   adjective

   Describing the space consisting of all linear functionals defined on another given vector 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.

   Note

   Linear algebra's most familiar duality, met almost always in the phrase dual space and written V* for a space V. The adjective also takes the preposition to: Doug Fisher and Hans-J. Lenz write that a hyperplane in the sample space is dual to a subspace in the variable space. Each single functional inside such a space is also a dual in its own right.

10. 10
    nouncountable

    For a vector in an inner product space, the linear functional that corresponds to taking the inner product with that same vector.

    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.

    Note

    Here the noun names a single object rather than a whole space. Each vector in an inner product space has its own dual, the functional that takes inner products with it. Gathered together, these duals make up the dual space. The Riesz representation theorem is what makes this vector-to-functional correspondence so central, and the plural, duals, is common in this sense.

11. 11
    nouncountable

    For a regular polyhedron, the polyhedron obtained by swapping the roles of vertices and faces, so that faces become corners and corners become faces.

    Builders of geometric models often pair a solid with its dual.

    The dual of the icosahedron is the dodecahedron.

    Note

    Geometry's dual is a partner solid, and the noun takes of: the octahedron is the dual of the cube. To build it, place a vertex at the center of each face of the original, so that the counts of vertices and faces trade places. The pairing is mutual, since the cube is equally the dual of the octahedron, which is why such solids are spoken of as dual pairs.

12. 12
    adjective

    Describing a category that contains the same objects as another but has the direction of every morphism reversed.

    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.

    Similaropposite

    Note

    Category theory's version, also called the opposite category and written with a superscript op. Its value is a bargain: as Colin McLarty puts it in Elementary Categories, Elementary Toposes (1992), every category is dual to its own dual. A statement true in all categories therefore brings its dual statement along for free. In this setting, opposite and dual are used interchangeably.

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