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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.

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## Some Related Sentences

Conversely and every

__Conversely__

**,**

__every__point on

**the**line can

**be**interpreted

**as**

**a**number

**in**an

**ordered**continuum which includes

**the**real numbers

**.**

__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__

**,**

__every__formally real field can

**be**equipped with

**a**compatible total order

**,**that will turn it into an

**ordered**field

**.**

__Conversely__

**,**

__every__preorder

**is**

**the**reachability relationship

**of**

**a**directed graph ( for instance

**,**

**the**graph that has an edge from x

**to**y for

__every__pair ( x

**,**y ) with x ≤ y ).

__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__

**,**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__

__every__positive functional φ gives

**a**corresponding inner product < ƒ

**,**g >< sub > φ </ sub > = φ ( g * ƒ ).

__Conversely__

**,**

__every__positive semi-definite matrix

**is**

**the**covariance matrix

**of**some multivariate distribution

**.**

We define Thm ( C )

**to****be****the****set****of**all formulas that are valid**in**C**.**__Conversely__**,**if X**is****a****set****of**formulas**,**let Mod ( X )**be****the**class**of**all frames which validate__every__formula from X**.**__Conversely__

**,**if we pick

__every__member

**of**

**the**same population with property

**and**ask " what proportion

**of**these have property?

__Conversely__

**,**

__every__admissible statistical procedure

**is**either

**a**Bayesian procedure or

**a**limit

**of**Bayesian procedures

**.**

As stated earlier

**,**an adjunction between categories C**and**D gives rise**to****a**family**of**universal morphisms**,**one for each object**in**C**and**one for each object**in**D**.**__Conversely__**,**if there exists**a**universal morphism**to****a**functor G: C → D from__every__object**of**D**,**then G has**a**left adjoint**.**
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__

**,**

__every__Polish space

**is**homeomorphic

**to**

**a**G < sub > δ </ sub >- subset

**of**

**the**Hilbert cube

**.**

__Conversely__

**,**extra lives are earned by collecting heart points

**,**which are earned by defeating enemies or collecting Hearts

**,**with an extra life earned for

__every__100 points earned

**.**

__Conversely__

**the**building can

**be**recovered from

**the**BN pair

**,**so that

__every__BN pair canonically defines

**a**building

**.**

__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 and lattice

__Conversely__

**,**any pair

**of**

__lattice__points with

**this**property constitute

**a**fundamental pair

**,**

**and**furthermore

**,**they generate

**the**same

__lattice__

**.**

Conversely and is

__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__

**,**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__

**,**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__

**,**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__

**,**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__

**,**

**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**.**0.195 seconds.