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Every non-zero number x, real or complex, has n different complex number nth roots including any positive or negative roots, see complex roots below.

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## Some Related Sentences

Every and non-zero

__Every__field of either type can be realized as the field of fractions of a Dedekind domain in which every

__non-zero__ideal is of finite index

**.**

( 3 )

__Every__unitary representation of G that**has**an ( ε**,**K )- invariant unit vector for**any**ε > 0 and**any**compact subset K**,****has**a__non-zero__invariant vector**.**

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 x

__Every__Hilbert space X is a Banach space because

**,**by definition

**,**a Hilbert space is complete with respect to the norm associated with its inner product

**,**where a norm and an inner product are said to be associated if for all

__x__∈ X

**.**

*

__Every__pair of congruence relations for an unknown integer__x__**,**of the form__x__≡ k ( mod a ) and__x__≡ l ( mod b ),**has**a solution**,**as stated by the Chinese remainder theorem ; in fact the solutions are described by a single congruence relation modulo ab**.**
*

__Every__finite topological space gives rise to a preorder on its points**,**in which__x__≤ y if and only if__x__belongs to every neighborhood of y**,**and every finite preorder can be formed as the specialization preorder of a topological space in this way**.**__Every__such line meets the sphere of radius one centered in the origin exactly twice

**,**say in P = (

__x__

**,**y

**,**z ) and its antipodal point (−

__x__

**,**− y

**,**− z ).

__Every__locally constant function from the

**real**numbers R to R is constant by the connectedness of R

**.**But the function f from the rationals Q to R

**,**defined by f (

__x__) = 0 for

__x__< π

**,**and f (

__x__) = 1 for

__x__> π

**,**is locally constant ( here we use the fact that π is irrational and that therefore the two sets

__Every__empty function is constant

**,**vacuously

**,**since there are no

__x__and y in A for which f (

__x__) and f ( y ) are

**different**when A is the empty set

**.**

__Every__

**real**

**number**

__x__is surrounded by an infinitesimal " cloud " of hyperreal numbers infinitely close to it

**.**

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