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Conversely, every formally real field can be equipped with a compatible total order, that will turn it into an ordered field.

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## Some Related Sentences

Conversely and every

__Conversely__

**,**

__every__point on the line

**can**

**be**interpreted as

**a**number in

**an**

**ordered**continuum which includes the

**real**numbers

**.**

__Conversely__

__every__partition of comes from

**an**equivalence relation in this way

**,**according to which if and only if and belong to the same set of the partition

**.**

__Conversely__

**,**

__every__preorder is the reachability relationship of

**a**directed graph ( for instance

**,**the graph

**that**has

**an**edge from x to y for

__every__pair ( x

**,**y )

**with**x ≤ y ).

__Conversely__

**,**though

__every__president from Washington to John Quincy Adams

**can**

**be**definitely assigned membership in

**an**Anglican or Unitarian body

**,**the significance of these affiliations is often downplayed as unrepresentative of their true beliefs

**.**

__Conversely__

**,**birds of prey-which show distinct reverse sexual dimorphism — tend to

**be**monogamous for long periods or mate for life ; some species like the Snail kite

**will**choose new mates

__every__year

**,**polygyny is noted in many Harriers and polyandry has been observed in the Harris ' Hawk ( notable for being the only bird of prey to regularly live and hunt in family and social groups ) and the aforementioned Galapagos hawk

**.**

__Conversely__

__every__positive functional φ gives

**a**corresponding inner product < ƒ

**,**g >< sub > φ </ sub > = φ ( g * ƒ ).

__Conversely__

**,**

__every__positive semi-definite matrix is the covariance matrix of some multivariate distribution

**.**

We define Thm ( C ) to

**be**the set of all formulas**that**are valid in C**.**__Conversely__**,**if X is**a**set of formulas**,**let Mod ( X )**be**the class of all frames which validate__every__formula from X**.**__Conversely__

**,**if we pick

__every__member of the same population

**with**property and ask " what proportion of these have property?

__Conversely__

**,**

__every__admissible statistical procedure is either

**a**Bayesian procedure or

**a**limit of Bayesian procedures

**.**

As stated earlier

**,****an**adjunction between categories C and D gives rise to**a**family of universal morphisms**,**one for each object in C and one for each object in D**.**__Conversely__**,**if there exists**a**universal morphism to**a**functor G: C → D from__every__object of D**,**then G has**a**left adjoint**.**
It is

**a**fact**that**the ring is**a**principal ideal ring ;**that**is**,**for any ideal I in**,**there exists**an**integer n in I such**that**__every__element of I is**a**multiple of n**.**__Conversely__**,**the set of all multiples of**an**arbitrary integer n is necessarily**an**ideal**,**and is usually denoted by ( n ).
This ring is the endomorphism ring of A

**.**__Conversely__**,**__every__ring (**with**identity ) is the endomorphism ring of some object in some preadditive category**.**__Conversely__

**,**

__every__Polish space is homeomorphic to

**a**G < sub > δ </ sub >- subset of the Hilbert cube

**.**

__Conversely__

**,**extra lives are earned by collecting heart points

**,**which are earned by defeating enemies or collecting Hearts

**,**

**with**

**an**extra life earned for

__every__100 points earned

**.**

__Conversely__the building

**can**

**be**recovered from the BN pair

**,**so

**that**

__every__BN pair canonically defines

**a**building

**.**

__Conversely__

**,**the following characterization of derived functors holds: given

**a**family of functors R < sup > i </ sup >: A → B

**,**satisfying the above

**,**i

**.**e

**.**mapping short exact sequences to long exact sequences

**,**such

**that**for

__every__injective object I of A

**,**R < sup > i </ sup >( I )= 0 for

__every__positive i

**,**then these functors are the right derived functors of R < sup > 0 </ sup >.

Conversely and real

__Conversely__

**,**both owners of capital and labor profit in

__real__terms from

**an**increase in the capital endowment

**.**

__Conversely__

**,**given

**a**harmonic function

**,**

**it**is the

__real__part of

**an**analytic function

**,**( at least locally ).

__Conversely__

**,**if M is positive definite

**,**

**it**has

**an**eigendecomposition P < sup >− 1 </ sup > DP where P is unitary

**,**D diagonal

**,**and all diagonal elements of D are

__real__and positive

**.**

__Conversely__

**,**given any harmonic function in two dimensions

**,**

**it**is the

__real__part of

**an**analytic function

**,**at least locally

**.**

__Conversely__

**,**the DHT is equivalent to computing the DFT of x < sub > n </ sub > multiplied by 1 + i

**,**then taking the

__real__part of the result

**.**

__Conversely__

**,**for real-valued functions f ( t ), the Hartley transform is given from the Fourier transform's

__real__and imaginary parts:

__Conversely__

**,**enchantments are also used to describe spells

**that**cause no

__real__effects but deceive people

**,**either by directly affecting their thoughts or using some kind of illusions

**.**

__Conversely__

**,**Janet Maslin in The New York Times called the film " bold

**,**attention-getting and more than

**a**little facile

**,**

**a**stylish-looking film without the connective tissue to give

**it**

__real__depth

**.**

__Conversely__

**,**high powered engines commonly complete

**a**" 4th gear sweep " test in less than 10 seconds

**,**which is not

**a**reliable load condition as compared to operation in the

__real__world

**.**

__Conversely__

**,**if the probing stylus enters

**a**film thick enough to have several layers of nodules so

**it**cannot

**be**spread laterally

**,**or if

**it**enters on top of

**a**cobblestone in

**a**single layer

**,**then

**it**

**will**measure not only the

__real__hardness of the diamond bonding

**,**but

**an**apparent hardness even greater because the internal compressive stress in those nodules would provide further resistance to penetration of the material by the stylus

**.**

__Conversely__

**,**the GDC may

**order**the attachment of personal property valued up to $ 25

**,**000

**,**but has no authority to

**order**the attachment of

__real__estate

**,**no matter how low the value

**.**

__Conversely__

**,**

**it**has also been said

**that**the connection between virtual crimes and

__real__crimes are " tenuous at best: It is the link between

**a**brutal rape and

**a**fictional story of

**a**brutal rape

**.**

__Conversely__

**,**simply mocking one method might require far less configuration than setting up

**an**entire

__real__class and therefore reduce maintenance needs

**.**

__Conversely__

**,**

**a**very powerful political group may use its power for opportunistic purposes because

**it**knows

**that**criticism of such action has no

__real__effect (

**it**is possible to " get away

**with**

**it**").

Conversely and field

Given

**a**__field__ordering ≤ as in Def 1**,**the elements such**that**x ≥ 0 forms**a**positive cone of F**.**__Conversely__**,**given**a**positive cone P of F as in Def 2**,**one**can**associate**a****total**ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P**.**This**total**ordering ≤< sub > P </ sub > satisfies the properties of Def 1**.**__Conversely__

**,**those same crystals

**will**change about 0

**.**1 % of their static dimension when

**an**external electric

__field__is applied to the material

**.**

__Conversely__

**,**

**a**decrease in wavelength is called blueshift and is generally seen when

**a**light-emitting object moves toward

**an**observer or when electromagnetic radiation moves

**into**

**a**gravitational

__field__

**.**

__Conversely__

**,**

**a**spinning superconductor generates

**a**magnetic

__field__

**,**precisely aligned

**with**the spin axis

**.**

__Conversely__

**,**one

**can**consider the flux the more fundamental quantity and call the vector

__field__the flux density

**.**

Given

**a**vector space V over**a**__field__K**,**the span of**a**set S ( not necessarily finite ) is defined to**be**the intersection W of all subspaces of V which contain S**.**W is referred to as the subspace spanned by S**,**or by the vectors in S**.**__Conversely__**,**S is called**a**spanning set of W**.**__Conversely__

**,**the variant of speedball is played on

**a**smaller

__field__and has

**a**very fast pace (

**with**games lasting up to five minutes ).

for some real-valued functions

**a**and b depending**,**respectively**,**on x and y**.**__Conversely__**,**given any such pair of real-valued functions**,**there exists**a**vector__field__X satisfying 1**.**and 2**.**__Conversely__

**,**if is

**a**separable algebraic extension

**,**and if L is any intermediate

__field__

**,**then and are separable extensions

**.**

__Conversely__

**,**and precisely at the same time as the discovery of the " wikt: bordereau | bordereau " in the summer of 1894

**,**the first successful prototype of the highly advanced long-recoil Mle 1897 Canon de 75 modèle 1897 | French 75

__field__gun had just been tested in great secrecy

**.**

__Conversely__

**,**the open

__field__levels were played in

**an**isometric viewpoint

**,**

**with**checkered floors

**,**clouded backgrounds and

**a**waterfall

**.**

__Conversely__

**,**if all three lenses are used from distances such

**that**the face fills the

__field__

**,**the wide-angle

**will**

**be**used from closer

**,**making the nose larger

**,**and the telephoto

**will**

**be**used from farther

**,**making the nose smaller

**.**

__Conversely__

**,**the valuation on

**a**discrete valuation ring

**can**

**be**extended to

**a**valuation on the quotient

__field__giving

**a**discrete valued

__field__

**,**whose associated discrete valuation ring is just

**.**

__Conversely__

**,**such

**a**rational parameterization induces

**a**

__field__homomorphism of the

__field__of functions of V

**into**

**.**

__Conversely__

**,**the topological charge only makes sense in the

**ordered**phase and not at all in the disordered phase

**,**because in some hand-waving way there is

**a**" topological condensate " in the disordered phase which randomizes the

__field__from point to point

**.**

__Conversely__

**,**any effect observed in

**an**accelerated reference frame should also

**be**observed in

**a**gravitational

__field__of corresponding strength

**.**

__Conversely__

**,**when applying

**a**current ( along the y-axis ) and

**a**perpendicular magnetic

__field__( along the z-axis )

**a**temperature gradient appears along the x-axis

**.**

If f is unramified at

**a**point x**,**then f is quasi-finite at x**.**__Conversely__**,**if f is quasi-finite at x**,**and if also**,**the local ring of x in the fiber f < sup >− 1 </ sup >( f ( x )), is**a**__field__and**a**finite separable extension of κ ( f ( x )), then f is unramified at x .< ref > EGA IV < sub > 4 </ sub >, Théorème 17**.**4**.**1 .</ ref >__Conversely__

**,**any Galois extension of K of degree p equal to the characteristic of K is the splitting

__field__of

**an**Artin – Schreier polynomial

**.**

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