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* Conversely, corresponding to any partition of X, there exists an equivalence relation ~ on X.

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## Some Related Sentences

Conversely and corresponding

__Conversely__every positive functional φ gives a

__corresponding__inner product < ƒ

**,**g >< sub > φ </ sub > = φ ( g

*****ƒ ).

__Conversely__

**,**if a suitable notion

**of**parallel transport is available

**,**then a

__corresponding__connection can be obtained by differentiation

**.**

__Conversely__

**,**the

__corresponding__expression for computer

**,**powerful computers is preferred over

*****strong computers

**.**

__Conversely__

**,**if a set

**of**edges forms a forest

**,**then by repeatedly removing leaves from this forest it can be shown by induction that the

__corresponding__set

**of**columns is independent

**.**

__Conversely__

**,**

**any**effect observed in

**an**accelerated reference frame should also be observed in a gravitational field

**of**

__corresponding__strength

**.**

__Conversely__

**,**as with

**any**filter base

**,**the local basis allows

**to**get back the

__corresponding__neighbourhood filter as

**.**

__Conversely__

**,**while Bayes rules with respect

**to**proper priors are virtually always admissible

**,**generalized Bayes rules

__corresponding__

**to**improper priors need not yield admissible procedures

**.**

__Conversely__

**,**one could define a potential

__corresponding__

**to**pH as a potential difference between a solute and pH neutral water

**,**separated by porous membrane ( that is permeable

**to**hydrogen ions ).

__Conversely__

**,**

**an**increase in height without a

__corresponding__increase in airspeed will put the aircraft above a survivable un-cushioned impact height

**,**and eventually above a height where rotor inertia can be converted

**to**sufficient lift

**to**enable a survivable landing

**.**

Thus

**,**for example**,**a quantity**X**which is known**to**lie in the range can be represented by the affine form**,**for some k**.**__Conversely__**,**the form implies that the__corresponding__quantity**X**lies in the range**.**

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 partition

__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__

**,**from a partial order

**on**a

__partition__

**of**a set S one can construct a preorder

**on**S

**.**There is a 1-to-1 correspondence between preorders and pairs (

__partition__

**,**partial order ).

Conversely and X

__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

**.**

That is

**,**the motivational internalist believes that**there**is**an**internal**,**necessary connection between one's conviction that__X__ought**to**be done and one's motivation**to**do__X__**.**__Conversely__**,**the motivational externalist ( or moral externalist ) claims that**there**is no necessary**,**internal connection between moral convictions and moral motives**.**
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**.**
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 B satisfies both**of**the conditions 1 and 2**,**then**there**is a unique topology**on**__X__for which B is a base ; it is called the topology generated by B**.**__Conversely__

**,**if R is a symmetric

**relation**over a set

__X__

**,**one can interpret it as describing

**an**undirected graph with the elements

**of**

__X__as the vertices and the pairs in R as the edges

**.**

A hypergraph H may be represented by a bipartite graph BG as follows: the sets

__X__and E are the partitions**of**BG**,**and ( x < sub > 1 </ sub >, e < sub > 1 </ sub >) are connected with**an**edge if and only if vertex x < sub > 1 </ sub > is contained in edge e < sub > 1 </ sub > in H**.**__Conversely__**,****any**bipartite graph with fixed parts and no unconnected nodes in the second part represents some hypergraph in the manner described above**.**
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

__X__is projective

**,**then the pullback

**of**under the closed immersion

**of**

__X__into a projective space is very ample

**.**

__Conversely__

**,**a complete variety is close

**to**being a projective variety: Chow's lemma states that if

__X__is a complete variety

**,**

**there**is a projective variety Z and a birational morphism Z →

__X__

**.**

__Conversely__

**,**if

__X__is a Hausdorff space and ker f is a closed set

**,**then the coimage

**of**f

**,**if given the quotient space topology

**,**must also be a Hausdorff space

**.**

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