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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.

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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__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 Boolean

__Conversely__

**,**

**given**

**a**

__Boolean__

**ring**R

**,**

**we**define the join operation

**by**

**a**' b =

**a**

**+**b

**+**ab

**,**

**and**the meet operation as multiplication

**.**

__Conversely__

**,**

**given**any topological space X

**,**the collection of subsets of X that are clopen

**(**both closed

**and**open

**)**

**is**

**a**

__Boolean__

**algebra**

**.**

Conversely and ring

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 ).
This

__ring__**is**the endomorphism__ring__of**A****.**__Conversely__**,**every__ring__**(**with identity**)****is**the endomorphism__ring__of some object in some preadditive category**.**__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__

**,**the valuation on

**a**discrete valuation

__ring__

**can**be extended to

**a**valuation on the quotient field giving

**a**discrete valued field

**,**whose associated discrete valuation

__ring__

**is**just

**.**

__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__

**,**Haystacks was an accomplished wrestler

**,**

**and**he consequently took the majority of the decisions

**,**many

**by**countout

**(**as Humphrey often could not get himself back

**into**the

__ring__

**by**the count of 20 ).

Statement 4 then implies that

**a**basis of M / mM lifts to**a**minimal set of generators of M**.**__Conversely__**,**every minimal set of generators of M**is**obtained in this way**,****and**any two such sets of generators are related**by**an invertible matrix with entries in the__ring__**.**
If f

**is**unramified at**a**point**x****,**then f**is**quasi-finite at**x****.**__Conversely__**,****if**f**is**quasi-finite at**x****,****and****if**also**,**the local__ring__of**x**in the fiber f < sup >− 1 </ sup >( f**(****x**)),**is****a**field**and****a**finite separable extension of κ**(**f**(****x**)), then f**is**unramified at**x**.< ref > EGA IV < sub > 4 </ sub >, Théorème 17**.**4**.**1 .</ ref >__Conversely__

**,**every distributive lattice

**is**isomorphic to

**a**

__ring__of sets ; in the case of finite distributive lattices

**,**this

**is**Birkhoff's representation theorem

**and**the sets may be taken as the lower sets of

**a**partially ordered set

**.**

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**.**0.182 seconds.