[permalink] [id link]

Every real polynomial of odd degree has at least one real number as a root.

from
Wikipedia

## 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 polynomial

__Every__output

**of**an encoder can be described by its own transfer function, which is closely related to the generator

__polynomial__

**.**

*

__Every__**root****of****a**monic__polynomial__whose coefficients are algebraic integers is itself an algebraic integer**.**__Every__

__polynomial__in can be factorized into polynomials that are irreducible over F

**.**This factorization is unique up to permutation

**of**the factors and the multiplication

**of**the factors by nonzero constants from F ( because the ring

**of**polynomials over

**a**field is

**a**unique factorization domain whose units are the nonzero constant polynomials ).

__Every__delta operator '

**has**

**a**unique sequence

**of**" basic polynomials ",

**a**

__polynomial__sequence defined by three conditions:

*

__Every__irreducible closed subset**of**P < sup > n </ sup >( k )**of**codimension**one**is**a**hypersurface ; i**.**e., the zero set**of**some homogeneous__polynomial__**.**
*

__Every__Jacobi-like__polynomial__sequence can have its domain shifted and / or scaled so that its interval**of**orthogonality is, and**has**Q
*

__Every__Laguerre-like__polynomial__sequence can have its domain shifted, scaled, and / or reflected so that its interval**of**orthogonality is, and**has**Q =
*

__Every__Hermite-like__polynomial__sequence can have its domain shifted and / or scaled so that its interval**of**orthogonality is, and**has**Q__Every__field and every

__polynomial__ring over

**a**field ( in arbitrarily many variables ) is

**a**reduced ring

**.**

In mathematics, an integer-valued

__polynomial__( also known**as****a**numerical__polynomial__) P ( t ) is**a**__polynomial__whose value P ( n ) is an integer for every integer n**.**__Every____polynomial__with integer coefficients is integer-valued, but the converse is not true**.**

Every and odd

__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__rotation is the result

**of**reflecting in an even

**number**

**of**reflections in hyperplanes through the origin, and every improper rotation is the result

**of**reflecting in an

__odd__

**number**

**.**

__Every__2 years ( on

__odd__years ) the Glandore Classic Boat Regatta is held during the second week

**of**July

**.**

__Every__

__odd__year Glandore hosts its " Classic Boat Regatta " which takes place over the space

**of**

**a**week

**.**

__Every__

__odd__year ( i

**.**e., 2011 ), the race travels the south route from Ophir to Kaltag through the ghost town

**of**Iditarod

**.**

__Every__connected symmetric graph must thus be both vertex-transitive and edge-transitive, and the converse is true for graphs

**of**

__odd__

**degree**

**.**

__Every__year, conferences with topics pertaining to choral conductors are held-in even numbered years,

**a**division conference is held in each division, and in

__odd__numbered years,

**a**national conference takes place in

**a**major U

**.**S

**.**city

**.**

0.831 seconds.