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Wikipedia

## Some Related Sentences

Conversely and only

__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 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__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__

**,**

**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__

**,**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__

**,**

**the**symbol width could be set

**at**8

**,**even if

__only__values 0 and 1 are used ; these data would

__only__require

**a**2-color table

**.**

__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__

**,**Baptists are underrepresented

**,**

**a**reflection

**of**

**their**quite recent expansion

**in**numbers ; there has been

__only__one Roman Catholic president

**,**although they are currently

**the**largest single denomination

**,**and there have been no Lutheran

**,**Pentecostal

**,**or Latter Day Saint presidents

**.**

__Conversely__

**,**birds

**of**prey-which show distinct reverse sexual dimorphism — tend

**to**be monogamous for long periods or mate for life ; some species like

**the**Snail kite will choose new mates every year

**,**polygyny is noted

**in**

**many**Harriers and polyandry has been observed

**in**

**the**Harris ' Hawk ( notable for being

**the**

__only__bird

**of**prey

**to**regularly live and hunt

**in**family and social groups ) and

**the**aforementioned Galapagos hawk

**.**

__Conversely__

**,**

**a**metrizable space is separable if and

__only__if it is second countable

**,**

**which**is

**the**case if and

__only__if it is Lindelöf

**.**

__Conversely__

**,**jumper classes are scored objectively

**,**based entirely on

**a**numerical score determined

__only__by whether

**the**horse attempts

**the**obstacle

**,**clears it

**,**and finishes

**the**course

**in**

**the**allotted time

**.**

__Conversely__

**,**if children are found

**to**

__only__develope after undergoing treatment it would challenge

**the**traumagenic model

**.**

__Conversely__

**,**

**of**

**the**253 known stable nuclides

**,**

__only__five have both an odd number

**of**protons and odd number

**of**neutrons: hydrogen-2 ( deuterium ), lithium-6

**,**boron-10

**,**nitrogen-14

**,**and tantalum-180m

**.**

__Conversely__

**,**

**a**wing dam is

**a**structure that

__only__partly restricts

**a**waterway

**,**creating

**a**faster channel that resists

**the**accumulation

**of**sediment

**.**

__Conversely__

**,**

**a**small farm surrounding

**the**owner's dwelling is called

**a**smallholding and is generally focused on self-sufficiency

**with**

__only__

**the**surplus being sold

**.**

__Conversely__

**,**Hill would play

__only__47 games

**in**

**the**following four seasons due

**to**

**a**recurring ankle injury

**.**

__Conversely__

**,**even though nearly 60 percent

**of**voters selected

**the**Democratic Governor Gary Locke

**in**2000

**,**

**in**2004

**the**Democratic gubernatorial nominee Christine Gregoire received

__only__41 percent

**of**

**the**vote

**.**

__Conversely__

**,**North Korea refused

**to**speak

**in**

**the**context

**of**six-party talks

**,**stating that it would

__only__accept bilateral talks

**with**

**the**United States

**.**

__Conversely__

**,**following

**the**diurnal motion

**with**

**the**camera

**,**

**to**eliminate it on

**the**photograph

**,**can best be done

**with**an equatorial mount

**,**

**which**requires adjusting

**the**right ascension

__only__;

**a**telescope

**may**have

**a**motor

**to**do that automatically ( sidereal drive ).

Conversely and users

__Conversely__

**,**if

**a**source file's modification time is

**in**

**the**future

**,**it triggers unnecessary rebuilding

**,**

**which**

**may**inconvenience

__users__

**.**

__Conversely__

**,**

**the**ease and simplicity

**of**dBase presented

**a**challenge as

**its**

__users__became more expert and as professional programmers were drawn

**to**it

**.**

__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**

__users__

**of**some innovative pronunciations such as " Febuary " ( for February )

**may**regard

**the**historically ( and phonetically ) authentic version as

**a**pedantic spelling pronunciation

**.**

__Conversely__

**,**

__users__can

**only**view content

**at**or above

**their**own integrity level (

**a**monk

**may**read

**a**book written by

**the**high priest

**,**but

**may**not read

**a**pamphlet written by

**a**lowly commoner ).

__Conversely__

**,**overly long retention can overwhelm

__users__

**with**slow computers or network connections by making

**the**article

**lists**inordinately large

**.**

Conversely and interested

__Conversely__

**,**someone's " dance card is full " implies that even though they

**may**be

__interested__

**,**they have no time for another person

**.**

__Conversely__

**,**Gaddafi was more

__interested__

**in**

**a**complete merging

**of**Libya and Tunisia into

**the**Arab Islamic Republic

**.**

Conversely and given

__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__

**,**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__

**,**

__given__

**a**groupoid G

**in**

**the**algebraic sense

**,**let G < sub > 0 </ sub > be

**the**set

**of**all elements

**of**

**the**form x * x < sup >− 1 </ sup >

**with**x varying through G and define G ( x * x < sup >-1 </ sup >, y * y < sup >-1 </ sup >) as

**the**set

**of**all elements f such that y * y < sup >-1 </ sup > * f * x * x < sup >-1 </ sup > exists

**.**

__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 >.

Given

**a**field ordering ≤ as**in**Def 1**,****the**elements such that x ≥ 0 forms**a**positive cone**of**F**.**__Conversely__**,**__given__**a**positive cone P**of**F as**in**Def 2**,**one can associate**a**total ordering ≤< sub > P </ sub > by setting x ≤ y**to**mean y − x ∈ P**.**This total ordering ≤< sub > P </ sub > satisfies**the**properties**of**Def 1**.**__Conversely__

**,**

__given__

**a**harmonic function

**,**it is

**the**real part

**of**an analytic function

**,**(

**at**least locally ).

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**.**__Conversely__

**,**surveys conducted among living donors postoperatively and

**in**

**a**period

**of**five years following

**the**procedure have shown extreme regret

**in**

**a**majority

**of**

**the**donors

**,**who said that

__given__

**the**chance

**to**repeat

**the**procedure

**,**they would not

**.**

__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**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 ( 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

**.**

__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

**.**

__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__

**,**it is hard

**to**believe

**,**

__given__

**the**length and intensity

**of**

**the**struggle between Máel Sechnaill and Brian

**,**that

**the**High King would surrender his title without

**a**fight

**.**

__Conversely__

**,**an algorithm

**to**test for solvability

**in**arbitrary integers could be used

**to**test

**a**

__given__equation for solvability

**in**natural numbers by applying that supposed algorithm

**to**

**the**equation obtained from

**the**

__given__equation by replacing each unknown by

**the**sum

**of**

**the**squares

**of**four new unknowns

**.**

__Conversely__

**,**

**a**disease that is easily transmitted but has

**a**short duration might spread widely during 2002 but is likely

**to**have

**a**low prevalence

**at**any

__given__point

**in**2003 ( due

**to**

**its**short duration ) but

**a**high incidence during 2002 ( as

**many**people develop

**the**disease ).

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