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Conversely, suppose we are given ( U, V, W ) satisfying

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## Some Related Sentences

Conversely and suppose

:

__Conversely__**,**__suppose__that φ is a smooth real-valued function on M in a neighborhood of p. Since every smooth function has a local coordinate expression**,****we**may express φ as a function in the coordinates.

Conversely and we

__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.

If neither A nor B includes the idea of existence

**,**then " some A**are**B " simply adjoins A to B.__Conversely__**,**if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true**,**and__we__have an ontological proof of A's existence.__Conversely__

__we__have a b if and only if a < b or a ~ b. This is the reason for using the notation ""; "≤" can be confusing for a preorder that is not anti-symmetric

**,**it may suggest that a ≤ b implies that a < b or a

__Conversely__

**,**specifying the symmetry can define the structure

**,**or at least clarify what

__we__mean by an invariant

**,**geometric language in which to discuss it ; this is one way of looking at the Erlangen programme.

__Conversely__

**,**a scientific antirealist or instrumentalist argues that science does not aim

**(**or at least does not succeed

**)**at truth and that

__we__should not regard scientific theories as true.

__Conversely__

**,**if

__we__pick every member of the same population with property and ask " what proportion of these have property?

__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__

**,**

__we__understand Cleopatra at her death as the transcendent queen of “ immortal longings ” because the container of her mortality can no longer restrain her: unlike Antony

**,**she never melts

**,**but sublimates from her very earthly flesh to ethereal fire and air .”

__Conversely__

__we__come to understand Cleopatra in that the container of her mortality can no longer restrain her.

"

__Conversely__**,**Jeffrey Tucker of the Ludwig von Mises Institute has argued that " The whole scene — which anticipated so much of the technology__we__have today but**,**strangely**,**not email or texting — reflected the ethos of time: a love of progress and a vision of a future that stayed on course ...__Conversely__

**,**if

__we__accept that human beings do have

**(**libertarian or incompatibilist

**)**free will

**,**then

__we__must accept that the world is not entirely governed by natural law.

__Conversely__

**,**starting from this equivalence

__we__can recover

**U**as the composite Rel → Sup → Set of the forgetful functor for Sup with this embedding of Rel in Sup.

__Conversely__

**,**

__we__can deduce that a minority of the helots were Laconian

**,**thus making this the one and only revolt of their history.

__Conversely__

**,**

__we__will explore how insights from science can be useful

**,**not only to develop technology and improve our material comfort

**,**but to reduce the suffering of individuals

**,**families

**,**and society.

__Conversely__

**,**if

__we__say that Paul has the goal of going into graduate school

**,**he may not necessarily believe that he will be able to accomplish this.

__Conversely__

**,**

**given**a Hopf algebra whose coalgebra structure is

**given**above

**,**

__we__can recover a formal group law F from it.

__Conversely__

**,**

**given**a Boolean ring R

**,**

__we__define the join operation by a ' b = a + b + ab

**,**and the meet operation as multiplication.

__Conversely__

**,**

**given**a configuration of a conic and six lines which tangent to it in the plane

**,**

__we__may define the double cover of the plane ramified over the union of these 6 lines.

__Conversely__

**,**if the length-scale decreases and the physical parameters approach fixed values

**,**then

__we__have ultraviolet fixed points.

__Conversely__

**,**

**given**any element u ∈ F

**(**A

**)**

__we__may define a natural transformation Φ: Hom

**(**A ,–) → F via

__Conversely__

**,**in the limit

__we__have infinitely rapid

**,**or diabatic passage ; the configuration of the state remains unchanged:

__Conversely__

**,**if G contains a proper non-trivial normal subgroup N

**,**then the composition of the natural surjective group homomorphism G → G / N with the regular representation of G / N produces a representation π of G which has kernel N. Taking χ to be the character of some non-trivial subrepresentation of π

**,**

__we__have a character

**satisfying**the hypothesis in the direct statement above.

Conversely and are

__Conversely__

**,**experimenters would consider as impressive such statements as the following

**,**which

**,**if they turned out to be hits

**,**

__are__so unusual as to be really significant:

__Conversely__

**,**the vowel marks of the Tigrinya abugida and the Amharic abugida

**(**ironically

**,**the original source of the term " abugida ") have been so completely assimilated into their consonants that the modifications

__are__no longer systematic and have to be learned as a syllabary rather than as a segmental script.

__Conversely__

**,**most heat-treatable alloys

__are__precipitation hardening alloys

**,**which produce the opposite effects that steel does.

__Conversely__

**,**most realists

**(**specifically

**,**indirect realists

**)**hold that perceptions or sense data

__are__caused by mind-independent objects.

__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__

**,**the Belgian Blue's meat tenderness has been argued to be just as tender because there

__are__a large number of smaller muscle fibers.

__Conversely__

**,**because space is expanding

**,**and more distant objects

__are__receding ever more quickly

**,**light emitted by us today may never " catch up " to very distant objects.

__Conversely__

**,**certain general principles

**(**for example

**,**neighbourliness

**,**or charity

**)**

__are__seen to be universal and consistent.

__Conversely__

**,**modern biological sciences

**(**including even concepts such as molecular ecology

**)**

__are__intimately entwined and dependent on the methods developed through biotechnology and what is commonly thought of as the life sciences industry.

__Conversely__beetles

__are__prey of various invertebrates and vertebrates including insects

**,**fish

**,**reptiles

**,**birds and mammals.

__Conversely__

**,**factors that favor plate columns

__are__: presence of solids in feed

**,**high liquid rates

**,**large column diameters

**,**complex columns

**,**columns with wide feed composition variation

**,**columns with a chemical reaction

**,**absorption columns

**,**columns limited by foundation weight tolerance

**,**low liquid rate

**,**large turn-down ratio and those processes subject to process surges.

__Conversely__

**,**computer implementations

__are__significant in applying ideas from discrete mathematics to real-world problems

**,**such as in operations research.

__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__

**,**Harris maintains that the fact-value distinction is a confusion

**,**proposing that values

__are__really a certain kind of fact.

__Conversely__

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

__are__often expressed in the more convenient inverse picoseconds.

__Conversely__

**,**BBC critic Mark Kermode believes that " the movie industries of Britain and America

__are__inextricably intertwined ", citing numerous examples of how Hollywood provides work to British production staff and studios

**,**whilst Britain enables Hollywood to base their prestigious productions at UK studios.

__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__

**,**rifle bullets can pierce light armor and

__are__easier to shoot accurately

**,**but even a carbine such as the Colt M4 is larger and / or longer than a submachine gun

**,**making it harder to maneuver in close quarters.

__Conversely__

**,**if either of these last two expressions is defined

**,**then so is the other

**(**and again they

__are__equal ).

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