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Every positive real number x has a single positive nth root, which is written.

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## Some Related Sentences

Every and positive

__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

**.**

__Every__line of

**a**GEDCOM file begins with

**a**level

**number**where all top-level records ( HEAD

**,**TRLR

**,**SUBN

**,**and each INDI

**,**FAM

**,**OBJE

**,**NOTE

**,**REPO

**,**SOUR

**,**and SUBM ) begin with

**a**line with level 0

**,**while other level numbers are

__positive__integers

**.**

*

__Every____positive__integer can be**written**as the sum of 73 or fewer sixth powers ( see Waring's problem ).__Every__

__positive__integer can be expressed as the sum of at most 19 fourth powers ; every sufficiently large integer can be expressed as the sum of at most 16 fourth powers ( see Waring's problem ).

A finitely-generated abelian group

**is**indecomposable if and only if it**is**isomorphic to Z or to**a**factor group of the form for some prime**number**p and some__positive__integer n**.**__Every__finitely-generated abelian group**is****a**direct sum of ( finitely many ) indecomposable abelian groups**.**__Every__C *- algebra

**has**an approximate identity of

__positive__elements of norm ≤ 1 ; indeed

**,**the net of all

__positive__elements of norm ≤ 1 ; in A with its natural order always suffices

**.**

'

__Every____positive__law**,**or every law simply and strictly so called**,****is**set**,**directly or circuitously**,**by**a**sovereign person or body**,**to**a**member or members of the independent political society wherein that person or body**is**supreme**.**__Every__residue class in this group contains exactly one square free integer

**,**and it

**is**common

**,**therefore

**,**only to consider square free

__positive__integers

**,**when speaking about congruent numbers

**.**

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

**.**

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