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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.

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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 R

__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 >.

**

__Conversely__**,****if**ƒ: I →__R__**is**absolutely continuous**and**thus differentiable almost everywhere**,****and**satisfies | ƒ ′( x )| ≤ K for almost all x**in**I**,**then ƒ**is**Lipschitz continuous**with**Lipschitz constant at most K**.**__Conversely__

**,**

**it**

**is**possible to 2-colour

**a**K < sub > 5 </ sub > without creating any monochromatic K < sub > 3 </ sub >, showing that

__R__( 3

**,**3 ) > 5

**.**

__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__

**,**

**the**following characterization

**of**derived functors holds: given

**a**family

**of**functors

__R__< sup > i </ sup >: A → B

**,**satisfying

**the**above

**,**i

**.**e

**.**mapping short exact sequences to long exact sequences

**,**such that for every injective object I

**of**A

**,**

__R__< sup > i </ sup >( I )= 0 for every positive i

**,**then these functors are

**the**right derived functors

**of**

__R__< sup > 0 </ sup >.

__Conversely__

**,**given

**a**Boolean ring

__R__

**,**we define

**the**join operation by

**a**' b =

**a**+ b + ab

**,**

**and**

**the**meet operation

**as**multiplication

**.**

__Conversely__

**,**

**if**this identity holds

**in**

**a**ring

__R__for all

**pairs**

**of**

**elements**

**a**

**and**b

**of**

**the**ring

**,**then

__R__

**is**commutative

**.**

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**.**0.127 seconds.