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Conversely, given any element u ∈ F ( A ) we may define a natural transformation Φ: Hom ( A ,–) → F via

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## Some Related Sentences

Conversely and given

__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__

**,**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__

**,**

__given__

**a**groupoid G in the algebraic sense

**,**let G < sub > 0 </ sub > be the set of all elements of the form x * x < sup >− 1 </ sup > with x varying through G and

**define**G

**(**x * x < sup >-1 </ sup >, y * y < sup >-1 </ sup >) as the set of all elements f such that y * y < sup >-1 </ sup > * f * x * x < sup >-1 </ sup > exists.

__Conversely__

**,**

__given__central idempotents

**a**< sub > 1 </ sub >,...,

**a**< sub > n </ sub > in R that are pairwise orthogonal and have sum 1

**,**then R is the direct sum of the rings Ra < sub > 1 </ sub >,…, Ra < sub > n </ sub >.

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__

**,**only the wiki users interested in

**a**

__given__project need look at its associated wiki pages

**,**in contrast to high-traffic mailing lists which

**may**burden subscribers with many messages

**,**regardless of their relevance.

__Conversely__

**,**

__given__

**a**harmonic function

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

**,**

**(**at least locally ).

Each convex set containing X must

**(**by the assumption that it is convex**)**contain all convex combinations of points in X**,**so the set of all convex combinations is contained in the intersection of all convex sets containing X.__Conversely__**,**the set of all convex combinations is itself**a**convex set containing X**,**so it also contains the intersection of all convex sets containing X**,**and therefore the sets__given__by these two definitions must be equal.__Conversely__

**,**surveys conducted among living donors postoperatively and in

**a**period of five years following the procedure have shown extreme regret in

**a**majority of the donors

**,**who said that

__given__the chance to repeat the procedure

**,**they would not.

__Conversely__

**,**

__given__an ordered tree

**,**and conventionally draw the root at the top

**,**then the child nodes in an ordered tree can be drawn left-to-right

**,**yielding an essentially unique planar embedding

**(**up to embedded homotopy

**,**i. e., moving the edges and nodes without crossing ).

__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

**(**

**A**

**,**m

**,**e

**,**inv

**)**is

**a**group object in one of those categories

**,**then m necessarily coincides with the

__given__operation on

**A**

**,**e is the inclusion of the

__given__identity

**element**on

**A**

**,**inv is the inversion operation and

**A**with the

__given__operation is an abelian group.

__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.

__Conversely__

**,**

__given__

**any**ring

**,**

**we**can form

**a**category by taking objects

**A**< sub > n </ sub > indexed by the set of

**natural**numbers

**(**including zero

**)**and letting the hom-set of morphisms from to be the set of-by-matrices over

**,**and where composition is

__given__by matrix multiplication.

__Conversely__

**,**it is hard to believe

**,**

__given__the length and intensity of the struggle between Máel Sechnaill and Brian

**,**that the High King would surrender his title without

**a**fight.

__Conversely__

**,**an algorithm to test for solvability in arbitrary integers could be used to test

**a**

__given__equation for solvability in

**natural**numbers by applying that supposed algorithm to the equation obtained from the

__given__equation by replacing each unknown by the sum of the squares of four new unknowns.

__Conversely__

**,**

**a**disease that is easily transmitted but has

**a**short duration might spread widely during 2002 but is likely to have

**a**low prevalence at

**any**

__given__point in 2003

**(**due to its short duration

**)**but

**a**high incidence during 2002

**(**as many people develop the disease ).

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__

**,**

__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.

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 ).0.091 seconds.