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Conversely, any algebra whose associator is alternating 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 whose

__Conversely__

**,**the existence of Bletchley Park

**,**and of the decrypting achievements there

**,**was never officially shared with the Soviet Union

**,**

__whose__war effort would have greatly benefited from regular decrypting of German messages relating to the Eastern Front

**.**

__Conversely__

**,**since Imhotep was known as the " Son of Ptah ," his mother was sometimes claimed to be Sekhmet

**,**the patron of Upper Egypt

__whose__consort was Ptah

**.**

__Conversely__

**,**citizens may find themselves ineligible because they do not currently reside within the United States ; exceptions apply for children of military parent ( s ) who were born overseas

**,**were disabled or became blind overseas

**,**or first applied for benefits overseas and for students studying abroad who were eligible for SSI in the month prior to leaving the US

**,**

__whose__absence will be for less than 1 year

**,**and who are studying to enhance their ability to perform substantial gainful activity

**,**sponsored by an educational institution in the US

**,**and would not be available to the individual in the US

**.**

__Conversely__

**,**nominating the party leader

__whose__party maintains a plurality and who are already familiar with their party manifesto facilitates a smoother nomination process

**.**

Equipped with this notion of length

**,**a Riemannian manifold**is**a metric space**,**meaning that it has a distance function d ( p**,**q )__whose__value at a pair of points p and q**is**the distance from p to q**.**__Conversely__**,**the metric tensor itself**is**the derivative of the distance function ( taken in a suitable manner ).__Conversely__

**,**nominating the party leader

__whose__party maintains a plurality and who are already familiar with their party manifesto facilitates a smoother nomination process

**.**

__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__this book

**,**

__whose__discovery

**is**touted in 2 Kings

**,**was therefore believed to have been of an early enough authorship to validate

**,**not only its inclusion

**,**but the book's ultimate placement as the 5th of the " Five Books of Moses ".

__Conversely__

**,**Clover points out that the villain of slasher films

**is**often a male

__whose__masculinity

**,**and sexuality more generally

**,**are in crisis

**.**

To a graph G there corresponds a signed complete graph Σ on the same vertex set

**,**__whose__edges are signed negative if in G and positive if not in G**.**__Conversely__**,**G**is**the subgraph of Σ that consists of all vertices and all negative edges**.**__Conversely__

**,**in the United States Navy

**,**the term " shipmate " can be the derogatory term used by officers and senior enlisted to refer to a sailor

__whose__name they have not bothered to remember or read off of their uniform ( Example: Hey!

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