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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.

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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 m

__Conversely__

**,**

**a**square flat plate

**of**area 1

__m__< sup > 2 </ sup > will have

**an**RCS

**of**< span style =" white-space: nowrap "> σ

__Conversely__

**,**when games

**on**

**the**West Coast are played at 10 p

**.**

__m__

**.**ET / 7 p

**.**

__m__

**.**PT

**,**many fans

**on**

**the**East Coast are unable to watch

**a**game

**in**its entirety

**,**due to games ending around 1

**a**

**.**

__m__

**.**ET / 10 p

**.**

__m__

**.**PT

**,**while most West Coast fans are able to watch

**the**entire game

**.**

__Conversely__

**,**

**the**river becomes narrower

**and**deeper through

**the**Highlands

**,**reaching its deepest point

**of**216 feet

**(**66

__m__), near Garrison

**.**

I ’

__m__longing to set me down shorely**and**raise my chaps proper**(**50 – 51 ).”__Conversely__**,**her husband Brack**is**committed to**the**mines**and**answers her as**the**family provider: “ It was never meant for**a**body to be full content**on****the**face**of**this earth**.**

Conversely and e

__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__

**,**when

**the**carbon dioxide levels

**in**

**the**blood decrease

**(**i

**.**

__e__.,

**in**

**the**lung capillaries ), carbon dioxide

**and**protons are released from hemoglobin

**,**increasing

**the**oxygen affinity

**of**

**the**protein

**.**

__Conversely__

**,**frequencies used for some railway electrification systems were much lower

**(**

__e__

**.**g

**.**16

**.**7 Hz

**and**25 Hz

**)**than normal utility frequencies

**(**50 – 60 Hz

**)**for historical reasons concerned mainly

**with**

**the**limitations

**of**early electric traction motors

**.**

__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**definition

**of**" unauthorized practice

**of**law "

**is**variable

**,**

**and**

**is**often conclusory

**and**tautological

**,**i

**.**

__e__., it

**is**

**the**doing

**of**

**a**lawyer's or counselor's work by

**a**non-lawyer for money

**.**

__Conversely__

**,**older speakers

**in**some regions

**(**such as

**the**American South

**)**may use

**in**words like coach

**and**road that have

**in**SE

**(**i

**.**

__e__

**.**

**,**).

__Conversely__

**,**once

**a**basis for

**A**has been chosen

**,**

**the**products

**of**basis elements can be set arbitrarily

**,**

**and**

**then**extended

**in**

**a**unique way to

**a**bilinear operator

**on**

**A**

**,**i

**.**

__e__., so

**the**resulting multiplication satisfies

**the**algebra laws

**.**

**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

**.**

__Conversely__

**,**

**if**waves

**of**different frequencies are not coherent

**,**

**then**

**,**when combined

**,**they create

**a**wave that

**is**continuous

**in**time

**(**

__e__

**.**g

**.**white light or white noise ).

__Conversely__

**,**using

**the**last line as

**a**definition

**one**shows that

**the**expression so defined

**is**

**a**connection compatible

**with**

**the**metric

**,**i

**.**

__e__

**.**

**is**

**a**Levi-Civita connection

**.**

__Conversely__

**,**some bachelor's degrees

**in**

**the**higher faculties

**(**i

**.**

__e__.,

**those**other than arts

**)**at

**those**universities are postgraduate qualifications

**(**

__e__

**.**g.,

**the**BCL

**and**BMus at Oxford ).

__Conversely__

**,**users can view content only at or below their own security level

**(**i

**.**

__e__

**.**secret researchers can view public or secret files

**,**but may not view top-secret files ; no read-up ).

__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 >.

which are linearly independent at each point q

**in**U**.**__Conversely__**,****given**such**a**coframe**,**there**is****a**unique moving frame X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub > which**is**dual to it**,**i**.**__e__., satisfies**the**duality relation α < sup > i </ sup >( X < sub > j </ sub >) = δ < sup > i </ sup >< sub > j </ sub >, where δ < sup > i </ sup >< sub > j </ sub >**is****the**Kronecker delta function**on**U**.**__Conversely__

**,**

**a**polynomial time algorithm

**(**

__e__

**.**g.,

**one**that requires n < sup > 20 </ sup > steps for n-digit keys

**)**may be too slow for any practical use

**.**

__Conversely__' to

**the**degree to which

**the**shadow

**is**recognised

**and**integrated

**,**

**the**problem

**of**

**the**anima

**,**i

**.**

__e__.,

**of**relationship

**,**

**is**constellated ',

**and**becomes

**the**centre

**of**

**the**individuation quest

**.**

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