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dual

[doo-uh l, dyoo-] /ˈdu əl, ˈdyu-/
adjective
1.
of, relating to, or noting two.
2.
composed or consisting of two people, items, parts, etc., together; twofold; double:
dual ownership; dual controls on a plane.
3.
having a twofold, or double, character or nature.
4.
Grammar. being or pertaining to a member of the category of number, as in Old English, Old Russian, or Arabic, that denotes two of the things in question.
noun, Grammar
5.
the dual number.
6.
a form in the dual, as Old English git “you two,” as contrasted with ge “you” referring to three or more.
Origin of dual
1535-1545
1535-45; < Latin duālis containing two, relating to a pair, equivalent to du(o) two + -ālis -al1
Related forms
dually, adverb
Can be confused
dual, duel.
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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British Dictionary definitions for dual

dual

/ˈdjuːəl/
adjective
1.
relating to or denoting two
2.
twofold; double
3.
(in the grammar of Old English, Ancient Greek, and certain other languages) denoting a form of a word indicating that exactly two referents are being referred to
4.
(maths, logic) (of structures or expressions) having the property that the interchange of certain pairs of terms, and usually the distribution of negation, yields equivalent structures or expressions
noun
5.
(grammar)
  1. the dual number
  2. a dual form of a word
verb duals, dualling, dualled
6.
(transitive) (Brit) to make (a road) into a dual carriageway
Derived Forms
dually, adverb
Word Origin
C17: from Latin duālis concerning two, from duo two
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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Word Origin and History for dual
adj.

c.1600, from Latin dualis, from duo "two" (see two). Related: Dually.

Online Etymology Dictionary, © 2010 Douglas Harper
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dual in Technology
mathematics
Every field of mathematics has a different meaning of dual. Loosely, where there is some binary symmetry of a theory, the image of what you look at normally under this symmetry is referred to as the dual of your normal things.
In linear algebra for example, for any vector space V, over a field, F, the vector space of linear maps from V to F is known as the dual of V. It can be shown that if V is finite-dimensional, V and its dual are isomorphic (though no isomorphism between them is any more natural than any other).
There is a natural embedding of any vector space in the dual of its dual:
V -> V'': v -> (V': w -> wv : F)
(x' is normally written as x with a horizontal bar above it). I.e. v'' is the linear map, from V' to F, which maps any w to the scalar obtained by applying w to v. In short, this double-dual mapping simply exchanges the roles of function and argument.
It is conventional, when talking about vectors in V, to refer to the members of V' as covectors.
(1997-03-16)
The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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