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Every real number, rational or not, is equated to one and only one cut of rationals.

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## Some Related Sentences

Every and real

*

__Every____real__Banach algebra which**is**a division algebra**is**isomorphic**to**the reals**,**the complexes**,****or**the quaternions**.**
*

__Every__unital__real__Banach algebra with no zero divisors**,****and**in which every principal ideal**is**closed**,****is**isomorphic**to**the reals**,**the complexes**,****or**the quaternions**.**
*

__Every__commutative__real__unital Noetherian Banach algebra with no zero divisors**is**isomorphic**to**the__real__**or**complex numbers**.**
*

__Every__commutative__real__unital Noetherian Banach algebra ( possibly having zero divisors )**is**finite-dimensional**.**__Every__sequence that ran off

**to**infinity in the

__real__line will then converge

**to**∞ in this compactification

**.**

__Every__holomorphic function can be separated into its

__real__

**and**imaginary parts

**,**

**and**each

**of**these

**is**a solution

**of**Laplace's equation on R < sup > 2 </ sup >.

__Every__ordered field

**is**a formally

__real__field

**,**i

**.**e., 0 cannot be written as a sum

**of**nonzero squares

**.**

*

__Every__separable metric space**is**isometric**to**a subset**of**the ( non-separable ) Banach space l < sup >∞</ sup >**of**all bounded__real__sequences with the supremum norm ; this**is**known as the Fréchet embedding**.**__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__nonzero

__real__

**number**has a multiplicative inverse ( i

**.**e

**.**an inverse with respect

**to**multiplication ) given by (

**or**).

__Every__sedenion

**is**a

__real__linear combination

**of**the unit sedenions 1

**,**< var > e </ var >< sub > 1 </ sub >, < var > e </ var >< sub > 2 </ sub >, < var > e </ var >< sub > 3 </ sub >, ...,

**and**< var > e </ var >< sub > 15 </ sub >,

__Every__Riemann surface

**is**a two-dimensional

__real__analytic manifold ( i

**.**e., a surface ), but it contains more structure ( specifically a complex structure ) which

**is**needed for the unambiguous definition

**of**holomorphic functions

**.**

In his book Nirvana: The Stories Behind

__Every__Song**,**Chuck Crisafulli writes that the song " stands out in the Cobain canon as a song with a very specific genesis**and**a very__real__subject ".__Every__finite

**or**bounded interval

**of**the

__real__numbers that contains an infinite

**number**

**of**points must have at least

**one**point

**of**accumulation

**.**

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__

__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 and rational

__Every__

__rational__

**number**/ has two closely related expressions as a finite continued fraction

**,**whose coefficients can be determined by applying the Euclidean algorithm

**to**

**.**

*

__Every__free abelian group**is**torsion-free**,**but the converse**is****not**true**,**as**is**shown by the additive group**of**the__rational__numbers Q**.**__Every__

__rational__variety

**,**including the projective spaces

**,**

**is**rationally connected

**,**but the converse

**is**false

**.**

__Every__non-singular

__rational__surface can be obtained by repeatedly blowing up a minimal

__rational__surface

**.**

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