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Every dual number has the form z = a + bε with a and b uniquely determined real numbers.

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## Some Related Sentences

Every and dual

* Duality:

__Every__statement, theorem, or definition in category theory**has****a**__dual__which is essentially obtained by " reversing all**the**arrows ".__Every__finite-dimensional vector space is isomorphic to its

__dual__space, but this isomorphism relies on an arbitrary choice of isomorphism ( for example, via choosing

**a**basis

**and**then taking

**the**isomorphism sending this basis to

**the**corresponding

__dual__basis ).

__Every__finite-dimensional normed space is reflexive, simply because in this case,

**the**space, its

__dual__

**and**bidual all have

**the**same linear dimension, hence

**the**linear injection J from

**the**definition is bijective, by

**the**rank-nullity theorem

**.**

__Every__linear program

**has**

**a**

__dual__problem

**with**

**the**same optimal solution, but

**the**variables in

**the**

__dual__problem correspond to constraints in

**the**primal problem

**and**vice versa

**.**

*

__Every__metrisable locally convex space**with**continuous__dual__carries**the**Mackey topology, that is, or to put it more succinctly every Mackey space carries**the**Mackey topology__Every__planar graph

**has**an algebraic

__dual__, which is in general not unique ( any

__dual__defined by

**a**plane embedding will do ).

Every and number

The album's lead single, " She's

__Every__Woman " peaked at number-one on**the**Billboard Country Chart, however its follow-up single, " The Fever " (**a**cover of an Aerosmith song ) only peaked at__number__23, becoming Brooks's first released Country single to not chart on**the**Top 10**.**__Every__year

**the**International Labour Conference's Committee on

**the**Application of Standards examines

**a**

__number__of alleged breaches of international labour standards

**.**

__Every__LORAN chain in

**the**world uses

**a**unique Group Repetition Interval,

**the**

__number__of which, when multiplied by ten, gives how many microseconds pass between pulses from

**a**given station in

**the**chain

**.**

__Every__vector space

**has**

**a**basis,

**and**all bases of

**a**vector space have

**the**same

__number__of elements, called

**the**dimension of

**the**vector space

**.**

The second single from

**the**UK release was " With__Every__Heartbeat ", released in late July**and**reached__number__one on**the**UK singles chart**.**
#

__Every__simple path from**a**given node to any of its descendant leaves contains**the**same__number__of black nodes**.**__Every__non-negative

**real**

__number__

**a**

**has**

**a**unique non-negative square root, called

**the**principal square root, which is denoted by, where √ is called

**the**radical sign or radix

**.**

__Every__

__number__is thought of as

**a**decimal fraction

**with**

**the**initial decimal point omitted, which determines

**the**filing order

**.**

__Every__well-ordered set is

**uniquely**order isomorphic to

**a**unique ordinal

__number__, called

**the**order type of

**the**well-ordered set

**.**

__Every__twin prime pair except ( 3, 5 ) is of

**the**

**form**( 6n − 1, 6n

**+**1 ) for some natural

__number__n,

**and**

**with**

**the**exception of < var > n </ var >

**=**1, < var > n </ var > must end in 0, 2, 3, 5, 7, or 8

**.**

__Every__third odd

__number__is divisible by 3, which requires that no three successive odd

**numbers**can be prime unless one of them is 3

**.**

* Hardy

**and**Littlewood listed as their Conjecture I: "__Every__large odd__number__( n > 5 ) is**the**sum of**a**prime**and****the**double of**a**prime**.**__Every__nonzero

**real**

__number__

**has**

**a**multiplicative inverse ( i

**.**e

**.**an inverse

**with**respect to multiplication ) given by ( or ).

Every and has

__Every__woman

__has__had

**the**experience of saying no when she meant yes,

**and**saying yes when she meant no

**.**

__Every__detail in his interpretation

__has__been beautifully thought out,

**and**of these I would especially cite

**the**delicious laendler touch

**the**pianist brings to

**the**fifth variation ( an obvious indication that he is playing

**with**Viennese musicians ),

**and**

**the**gossamer shading throughout

**.**

__Every__family of Riviera Presbyterian Church

__has__been asked to read

**the**Bible

**and**pray together daily during National Christian Family Week

**and**to undertake one project in which all members of

**the**family participate

**.**

__Every__community, if it is alive

__has__

**a**spirit,

**and**that spirit is

**the**center of its unity

**and**identity

**.**

__Every__such subset

__has__

**a**smallest element, so to specify our choice function we can simply say that it maps each set to

**the**least element of that set

**.**

** Zorn's lemma:

__Every__non-empty partially ordered set in which every chain ( i**.**e**.**totally ordered subset )__has__an upper bound contains at least one maximal element**.**
The restricted principle "

__Every__partially ordered set__has__**a**maximal totally ordered subset " is also equivalent to AC over ZF**.**
** Tukey's lemma:

__Every__non-empty collection of finite character__has__**a**maximal element**with**respect to inclusion**.**
*

__Every__continuous functor on**a**small-complete category which satisfies**the**appropriate solution set condition__has__**a**left-adjoint (**the**Freyd adjoint functor theorem ).__Every__unit of length

__has__

**a**corresponding unit of area, namely

**the**area of

**a**square

**with**

**the**given side length

**.**

__Every__field

__has__an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some

**form**of

**the**axiom of choice

**.**

__Every__ATM cell

__has__an 8-or 12-bit Virtual Path Identifier ( VPI )

**and**16-bit Virtual Channel Identifier ( VCI ) pair defined in its header

**.**

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