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Conversely, any algebra for which this is true is clearly alternative.

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## Some Related Sentences

Conversely and any

__Conversely__

**,**a subset R defines a binary function if and only if

**,**

**for**

__any__x in X and y in Y

**,**there exists a unique z in Z such that ( x

**,**y

**,**z ) belongs to R

**.**

__Conversely__the equilibrium position

**is**said to be " far to the left " if hardly

__any__product

**is**formed from the reactants

**.**

* The spectrum of

__any__bounded linear operator on a Banach space**is**a nonempty compact subset of the complex numbers C**.**__Conversely__**,**__any__compact subset of C arises in**this**manner**,**as the spectrum of some bounded linear operator**.**__Conversely__

**,**there are other stars that never rise above the horizon

**,**as seen from

__any__given point on the Earth's surface ( except exactly on the equator ).

__Conversely__

**,**

__any__surjection between sets determines a partition on its domain

**,**the set of preimages of singletons in the codomain

**.**

__Conversely__

**,**Derek Bickerton and others argue that the advent of abstract words provided a mental basis

**for**analyzing higher-order relations

**,**and that

__any__communication system that remotely resembles human language utterly relies on cognitive architecture that co-evolved alongside language

**.**

__Conversely__

**,**a person may feel like he belongs to one state without having

__any__legal relationship to it

**.**

__Conversely__

**,**the interior of the box has a constant

**,**zero potential energy .< ref > Actually

**,**

__any__constant

**,**finite potential can be specified within the box

**.**

__Conversely__

**,**extremely thin jewelry can cause the same tearing in what

**is**commonly referred to as the " cheese cutter effect ", either during sudden torsion or over a long period of wearing

**,**especially if the thin jewelry bears

__any__weight

**.**

__Conversely__

**,**

__any__Hermitian positive semidefinite matrix M can be written as M = A < sup >*</ sup > A ;

**this**

**is**the Cholesky decomposition

**.**

__Conversely__

**,**if a double sharp were added to

__any__other note not containing a sharp or flat as indicated by the key signature then the note will be raised two semitones or a whole step with respect to the chromatic scale

**.**

__Conversely__

**,**supplementation with L-phenylalanine

**,**L-tyrosine

**,**L-DOPA

**,**or

__any__of the cofactors will increase their respective concentrations

**.**

__Conversely__

**,**

__any__choice of μ

**,**full rank matrix U

**,**and positive diagonal entries Λ < sub > i </ sub > yields a non-singular multivariate normal distribution

**.**

__Conversely__

**,**the influence of the data at

__any__given point on the initial line propagates with the finite velocity c: there

**is**no effect outside a triangle through that point whose sides are characteristic curves

**.**

__Conversely__

**,**given

__any__harmonic function in two dimensions

**,**it

**is**the real part of an analytic function

**,**at least locally

**.**

__Conversely__

**,**if the Turing Machine

**is**expected polynomial-time (

**for**

__any__given x ), then a considerable fraction of the runs must be polynomial-time bounded

**,**and the coin sequence used in such a run will be a witness

**.**

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 ).

Conversely and algebra

__Conversely__

**,**if a Boolean ring A

**is**given

**,**we can turn it into a Boolean

__algebra__by defining x ∨ y := x + y + ( x · y ) and x ∧ y := x · y

**.**

__Conversely__

**,**many theorems that hold in universal

__algebra__do not generalise all the way to category theory

**.**

__Conversely__

**,**once a basis

**for**A has been chosen

**,**the products of basis elements can be set arbitrarily

**,**and then extended in a unique way to a bilinear operator on A

**,**i

**.**e., so the resulting multiplication satisfies the

__algebra__laws

**.**

__Conversely__

**,**given a Hopf

__algebra__whose coalgebra structure

**is**given above

**,**we can recover a formal group law F from it

**.**

__Conversely__

**,**given

**any**topological space X

**,**the collection of subsets of X that are clopen ( both closed and open )

**is**a Boolean

__algebra__

**.**

__Conversely__

**,**symmetric tensors are defined as invariants: given the natural action of the symmetric group on the tensor

__algebra__

**,**the symmetric tensors are the subspace on

**which**the symmetric group acts trivially

**.**

__Conversely__

**,**the normed division algebras immediately give rise to trialities by taking each V < sub > i </ sub > equal to the division

__algebra__

**,**and using the inner product on the

__algebra__to dualize the multiplication into a trilinear form

**.**

__Conversely__

**,**given

**any**Lie

__algebra__with a direct sum decomposition satisfying these three conditions

**,**the linear map σ

**,**equal to the identity on and minus the identity on

**,**

**is**an involutive automorphism

**.**

Conversely and for

__Conversely__

**,**if he gives a heavy rating to his own reading

**,**and finds more accurate facts in it than in the others

**,**a point

**is**chalked up

__for__the intrinsic

**,**objective meaningfulness of

**this**type of mediumistic material

**.**

__Conversely__

**,**some elements do not maintain distinct allotropes in different phases –

__for__example phosphorus has numerous solid allotropes

**,**

**which**all revert to the same P < sub > 4 </ sub > form when melted to the liquid state

**.**

__Conversely__

**,**British English favours fitted as the past tense of fit generally

**,**whereas the preference of American English

**is**more complex: AmEng prefers fitted

__for__the metaphorical sense of having made an object " fit " ( i

**.**e., suited )

__for__a purpose ; in spatial transitive contexts

**,**AmEng uses fitted

__for__the sense of having made an object conform to an unchanged object that it surrounds ( e

**.**g., " fitted X around Y ") but fit

__for__the sense of having made an object conform to an unchanged object that surrounds it ( e

**.**g., " fit X into Y "); and

__for__the spatial senses ( both intransitive and transitive ) of having been matching with respect to contour

**,**with no alteration of either object implied

**,**AmEng prefers fit (" The clothes fit

**.**

__Conversely__the use of

**true**brass seems to have declined in Western Europe during

**this**period in favour of gunmetals and other mixed alloys but by the end of the first Millennium AD brass artefacts are found in Scandinavian graves in Scotland

**,**brass was being used in the manufacture of coins in Northumbria and there

**is**archaeological and historical evidence

__for__the production of brass in Germany and The Low Countries areas rich in calamine ore

**which**would remain important centres of brass making throughout the medieval period

**,**especially Dinant – brass objects are still collectively known as dinanterie in French

**.**

__Conversely__

**,**many fighter aircraft

**,**such as the F-16

**,**are often used as ' bomb trucks ,' despite being designed

__for__aerial combat

**.**

__Conversely__

**,**certain general principles (

__for__example

**,**neighbourliness

**,**or charity ) are seen to be universal and consistent

**.**

__Conversely__

**,**in more recent times

**,**Russian existentialist philosopher Lev Shestov viewed Job as the embodiment of the battle between reason (

**which**offers general and seemingly comforting explanations

__for__complex events ) and faith in a personal god

**,**and one man's desperate cry

__for__him

**.**

__Conversely__

**,**the vast majority of early attempts at proper excavation techniques failed to accurately measure or record stratigraphy

**,**thereby failing to provide a secure context

__for__artefact finds making interpretations extremely limited in scope

**.**

__Conversely__

**,**in the English language as a whole

**,**singular verb forms can often be used with nouns ending in "- s " that were once considered plural (

__for__example: " Physics

**is**my favorite academic subject ").

__Conversely__

**,**the tiny meson mass mass differences responsible

__for__meson oscillations are often expressed in the more convenient inverse picoseconds

**.**

__Conversely__

**,**in functional code

**,**the output value of a function depends only on the arguments that are input to the function

**,**so calling a function f twice with the same value

__for__an argument x will produce the same result f ( x ) both times

**.**

__Conversely__

**,**the bodies of people who had certain medical conditions are useful

__for__research into those conditions

**.**

__Conversely__

**,**if the data are sparse — that

**is**

**,**if only K out of N Fourier coefficients are nonzero — then the complexity can be reduced to O ( K log N log ( N / K )), and

**this**has been demonstrated to lead to practical speedups compared to an ordinary FFT

__for__N / K > 32 in a large-N example ( N = 2 < sup > 22 </ sup >) using a probabilistic approximate algorithm (

**which**estimates the largest K coefficients to several decimal places ).

__Conversely__

**,**one might expect that inertial motions

**,**once identified by observing the actual motions of bodies and making allowances

__for__the external forces ( such as electromagnetism or friction ), can be used to define the geometry of space

**,**as well as a time coordinate

**.**

__Conversely__

**,**

__for__many deductive systems

**,**it

**is**possible to prove the completeness theorem as an effective consequence of the compactness theorem

**.**

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