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Conversely, any equation can take the canonical form f ( x ) = 0, so equation solving is the same thing as computing ( or finding ) a root of a function.

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## Some Related Sentences

Conversely and any

__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__

**the**equilibrium position

**is**said to be " far to

**the**left " if hardly

__any__product

**is**formed from

**the**reactants

**.**

* 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__

**,**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__

**,**

__any__surjection between sets determines

**a**partition on its domain

**,**

**the**set

**of**preimages

**of**singletons in

**the**codomain

**.**

__Conversely__

**,**Derek Bickerton and others argue that

**the**advent

**of**abstract words provided

**a**mental basis for analyzing higher-order relations

**,**and that

__any__communication system that remotely resembles human language utterly relies on cognitive architecture that co-evolved alongside language

**.**

__Conversely__

**,**

**a**person may feel like he belongs to one state without having

__any__legal relationship to it

**.**

__Conversely__

**,**

**the**interior

**of**

**the**box has

**a**constant

**,**zero potential energy .< ref > Actually

**,**

__any__constant

**,**finite potential

**can**be specified within

**the**box

**.**

__Conversely__

**,**extremely thin jewelry

**can**cause

**the**

**same**tearing in what

**is**commonly referred to

**as**

**the**" cheese cutter effect ", either during sudden torsion

**or**over

**a**long period

**of**wearing

**,**especially if

**the**thin jewelry bears

__any__weight

**.**

__Conversely__

**,**

__any__Hermitian positive semidefinite matrix M

**can**be written

**as**M

**=**A < sup >*</ sup > A ; this

**is**

**the**Cholesky decomposition

**.**

__Conversely__

**,**if

**a**double sharp were added to

__any__other note not containing

**a**sharp

**or**flat

**as**indicated by

**the**key signature then

**the**note will be raised two semitones

**or**

**a**whole step with respect to

**the**chromatic scale

**.**

__Conversely__

**,**supplementation with L-phenylalanine

**,**L-tyrosine

**,**L-DOPA

**,**

**or**

__any__

**of**

**the**cofactors will increase their respective concentrations

**.**

__Conversely__

**,**

__any__choice

**of**μ

**,**full rank matrix U

**,**and positive diagonal entries Λ < sub > i </ sub > yields

**a**non-singular multivariate normal distribution

**.**

__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

**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

**.**

It

**is****a**fact that**the**ring**is****a**principal ideal ring ; that**is****,**for__any__ideal I in**,**there exists an integer n in I such that every element**of**I**is****a**multiple**of**n**.**__Conversely__**,****the**set**of**all multiples**of**an arbitrary integer n**is**necessarily an ideal**,**and**is**usually denoted by**(**n ).

Conversely and equation

__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__

**,**when

**the**population

**is**large

**the**value

**of**approaches 1 effectively reducing

**the**terms inside

**the**brackets

**of**

__equation__1

**.**2 to zero

**.**

#

__Conversely__if u**is****a**solution**of**Laplace's__equation__**,**then there exist functions v which solve**the**Cauchy – Riemann equations together with u**.**__Conversely__

**,**starting with

**the**Schrödinger

__equation__and our < em > Ansatz </ em > for ', we arrive at

Conversely and can

__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__

**,**in

**the**English language

**as**

**a**whole

**,**singular verb forms

__can__often be used with nouns ending in "- s " that were once considered plural

**(**for example: " Physics

**is**my favorite academic subject ").

__Conversely__

**,**every point on

**the**line

__can__be interpreted

**as**

**a**number in an ordered continuum which includes

**the**real numbers

**.**

__Conversely__

**,**non-spontaneous electrochemical reactions

__can__be driven forward by

**the**application

**of**

**a**current at sufficient voltage

**.**

__Conversely__

**,**badly managed food aid

__can__create problems by disrupting local markets

**,**depressing crop prices

**,**and discouraging food production

**.**

__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__

**,**when one wants to compute an arbitrary number

**(**N

**)**

**of**discrete samples

**of**one cycle

**of**

**a**continuous DTFT

**,**it

__can__be done by

**computing**

**the**relatively simple DFT

**of**s < sub > N </ sub >,

**as**defined above

**.**

__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__

**,**one might expect that inertial motions

**,**once identified by observing

**the**actual motions

**of**bodies and making allowances for

**the**external forces

**(**such

**as**electromagnetism

**or**friction ),

__can__be used to define

**the**geometry

**of**space

**,**

**as**well

**as**

**a**time coordinate

**.**

__Conversely__

**,**

**a**high pH

**,**low CO < sub > 2 </ sub >,

**or**low 2

**,**3 BPG favors

**the**relaxed

**form**which

__can__better bind oxygen

**.**

__Conversely__

**,**

**a**very severe bit

**,**in

**the**right hands

**,**

__can__transmit subtle commands that cause no pain to

**the**horse

**.**

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__

**,**every formally real field

__can__be equipped with

**a**compatible total order

**,**that will turn it into an ordered field

**.**

__Conversely__

**,**if

**the**odds

**of**drawing

**a**winning card are numerically lower than

**the**pot odds

**,**

**the**call has

**a**negative expectation

**,**and you

__can__expect to win less money on average than it costs to call

**the**bet

**.**

__Conversely__

**,**from

**a**partial order on

**a**partition

**of**

**a**set S one

__can__construct

**a**preorder on S

**.**There

**is**

**a**1-to-1 correspondence between preorders and pairs

**(**partition

**,**partial order ).

__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__

**,**though every president from Washington to John Quincy Adams

__can__be definitely assigned membership in an Anglican

**or**Unitarian body

**,**

**the**significance

**of**these affiliations

**is**often downplayed

**as**unrepresentative

**of**their true beliefs

**.**

__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__

**,**water deep in

**the**ocean near geothermal vents

__can__reach temperatures

**of**hundreds

**of**degrees and remain liquid

**.**

__Conversely__

**,**AES

**is**sensitive to

**the**lighter elements

**,**and unlike X-ray fluorescence

**,**Auger peaks

__can__be detected for elements

**as**light

**as**lithium

**(**Z

**=**3 ).

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