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Every real number x is surrounded by an infinitesimal " cloud " of hyperreal numbers infinitely close to it.

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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**.**0.131 seconds.