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Conversely, if W is subspace of V, then W is itself a vector space under the operations induced by

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## Some Related Sentences

Conversely and if

__Conversely__

**,**

__if__statistics were uncovered which contradicted

**a**cherished theory

**,**

**the**sources were denounced as faulty.

__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__

**,**

__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__

**,**

**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__

**,**

__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__

**,**

__if__

**the**second theory

**is**correct

**,**

**then**

**the**Athenians were merely reacting to

**the**Persians attacking them.

__Conversely__

**the**equilibrium position

**is**said to be " far to

**the**left "

__if__hardly any product

**is**formed from

**the**reactants.

__Conversely__

**,**

__if__ƒ: C → C

**is**

**a**function which

**is**differentiable when regarded as

**a**function on R < sup > 2 </ sup >,

**then**ƒ

**is**complex differentiable

__if__and only

__if__

**the**Cauchy – Riemann equations hold.

__Conversely__

**,**

__if__

**the**amount

**of**fat

**is**increased

**,**increasing

**the**number

**of**calories ingested will only add weight.

__Conversely__

**,**

__if__

**the**source

**of**waves

**is**moving away from

**the**observer

**,**each wave

**is**emitted from

**a**position farther from

**the**observer than

**the**previous wave

**,**so

**the**arrival time between successive waves

**is**increased

**,**reducing

**the**frequency.

__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.

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__

**,**

__if__

**the**measured potential

**is**negative

**,**

**the**electrode

**is**more oxidizing than

**the**SHE ( such as Zn in ZnSO < sub > 4 </ sub > where

**the**standard electrode potential

**is**− 0. 76

**V**).

__Conversely__

**,**

__if__

**the**firm

**is**able to get bulk discounts

**of**an input

**,**

**then**it could have economies

**of**scale in some range

**of**output levels even

__if__it has decreasing returns in production in that output range.

__Conversely__

**,**daylight stock shot in daylight will look normal

**,**but orange

__if__shot

**under**tungsten lights.

__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 and W

Given

**a****vector****space****V**over**a**field K**,****the**span**of****a**set S ( not necessarily finite )**is**defined to be**the**intersection__W__**of**all subspaces**of****V**which contain S.__W__**is**referred to as**the****subspace**spanned**by**S**,**or**by****the**vectors in S.__Conversely__**,**S**is**called**a**spanning set**of**__W__.__Conversely__

**,**

**the**county lies entirely within New Jersey's 1st Legislative District

**,**which

**is**currently represented

**by**Senator Jeff Van Drew and Assemblymen Nelson T. Albano and Matthew

__W__. Milam

**,**all Democrats.

__Conversely__

**,**an exhaustive firing test

**of**

**the**M1918 Chauchat in. 30-06 was also carried out in 1994 near Chambersburg

**,**Pennsylvania

**,**

**by**R. Keller and

__W__. Garofalo.

Conversely and is

__Conversely__

**,**an adiabatic process that

__is__irreversible and extracts no work

__is__in an isenthalpic process

**,**such as viscous drag

**,**progressing towards

**a**nonnegative change in entropy.

__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__

**,**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__

**,**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__

**,**

**the**islands do not receive

**the**upwellings ( cold streams ) that affect

**the**West African coast

**,**so

**the**air temperature

__is__cooler than in Senegal

**,**but

**the**sea

__is__actually warmer

**,**because

**the**orographic relief

**of**some islands

**,**as Sao Miguel with steep mountains

**,**cover it with rich woods and luxuriant vegetation where

**the**dense moisture condense and soak

**the**plants

**,**rocks

**,**soil

**,**logs

**,**moss etc.

__Conversely__in francophone Canada

**,**one hundredth

**of**

**a**Canadian dollar

__is__informally called

**a**sou ( penny ), though cent

__is__official in both English and French.

__Conversely__

**,**an absence

**of**secure cycle-parking

__is__

**a**recurring complaint

**by**cyclists from cities with low modal share

**of**cycling.

* 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 and subspace

__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__

**,**

**if**f

**is**also an inclusion

**the**attaching construction

**is**to simply glue X and Y together along their common

__subspace__.

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