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Every binary relation R on a set S can be extended to a preorder on S by taking the transitive closure and reflexive closure, R < sup >+=</ sup >.

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## Some Related Sentences

Every and relation

*

__Every__pair of congruence relations for an unknown integer x**,**of**the**form x ≡ k ( mod**a**)**and**x ≡ l ( mod b ), has**a**solution**,**as stated**by****the**Chinese remainder theorem ; in fact**the**solutions are described**by****a**single congruence__relation__modulo ab.__Every__congruence

__relation__has

**a**corresponding quotient structure

**,**whose elements are

**the**equivalence classes ( or congruence classes ) for

**the**

__relation__.

__Every__peculiarity of diction

**,**every particle

**,**every sign

**,**is

**to**

**be**considered as of higher importance

**,**as having

**a**wider

__relation__

**and**as being of deeper meaning than it seems

**to**have.

__Every__constraint is in turn

**a**pair ( usually represented as

**a**matrix ), where is an-tuple of variables

**and**is an-ary

__relation__

**on**.

__Every__day

**,**having hardly finished working in

**the**surgery room

**,**Favaloro would spend hours

**and**hours reviewing coronary angiograms

**and**studying coronary arteries

**and**their

__relation__with

**the**cardiac muscle.

__Every__employment

__relation__leaves

**the**employer with

**a**residue of discretion

**,**historically expressed as

**the**‘ master-servant ’ relationship.

__Every__student is continuously evaluated

**,**corrected

**,**

**and**mentored

**,**with special attention paid

**to**

**the**smallest of details

**,**such as

**the**placement of

**a**finger within 1 / 4 inch of its required location along

**a**trouser seam

**,**angle of

**the**weapon

**,**

**and**positioning of

**the**student in

__relation__

**to**

**the**unit.

We express this

__relation__**by**means of**the**notation ∠( h**,**k ) ≅ ( h ′, k ′)__Every__angle is congruent**to**itself ; that is**,**∠( h**,**k ) ≅ ( h**,**k ) or ∠( h**,**k ) ≅ ( k**,**h )
" He continues: "

__Every__category ... every description of existence or__relation__**,**is necessarily**a**transcript from our own nature**and**our own experience.

Every and R

__Every__holomorphic function

**can**

**be**separated into its real

**and**imaginary parts

**,**

**and**each of these is

**a**solution of Laplace's equation

**on**

__R__

**<**

**sup**> 2 </

**sup**

**>.**

__Every__vector v in determines

**a**linear map from

__R__

**to**

**taking**1

**to**v

**,**which

**can**

**be**thought of as

**a**Lie algebra homomorphism.

* In any ring

__R__**,****a**maximal ideal is an ideal M that is maximal in**the****set**of all proper ideals of__R__**,**i. e. M is contained in exactly 2 ideals of__R__**,**namely M itself**and****the**entire ring__R__.__Every__maximal ideal is in fact prime.
*

__Every__separable metric space is isometric**to****a**subset of C (),**the**separable Banach space of continuous functions →__R__**,**with**the**supremum norm.__Every__simple R-module is isomorphic

**to**

**a**quotient

__R__/ m where m is

**a**maximal right ideal of

__R__. By

**the**above paragraph

**,**any quotient

__R__/ m is

**a**simple module.

__Every__random vector gives rise

**to**

**a**probability measure

**on**

__R__

**<**

**sup**> n </

**sup**> with

**the**Borel algebra as

**the**underlying sigma-algebra.

__Every__prime ideal P in

**a**Boolean ring

__R__is maximal:

**the**quotient ring

__R__/ P is an integral domain

**and**also

**a**Boolean ring

**,**so it is isomorphic

**to**

**the**field F

**<**sub > 2 </ sub >, which shows

**the**maximality of P. Since maximal ideals are always prime

**,**prime ideals

**and**maximal ideals coincide in Boolean rings.

*

__Every__left ideal I in__R__is finitely generated**,**i. e. there exist elements**a****<**sub > 1 </ sub >, ...,**a****<**sub > n </ sub > in I such that I = Ra**<**sub > 1 </ sub > + ... + Ra**<**sub > n </ sub**>.**
*

__Every__non-empty**set**of left ideals of__R__**,**partially ordered**by**inclusion**,**has**a**maximal element with respect**to****set**inclusion.__Every__year since 1982

**,**

**the**W. C. Handy Music Festival is held in

**the**Florence / Sheffield / Muscle Shoals area

**,**featuring blues

**,**jazz

**,**country

**,**gospel

**,**rock music

**and**

__R__& B.

__Every__adult citizen of this small settlement signed

**the**small petition ; E. K Dyer

**and**his wife

**,**William Johnson

**,**Joseph Otis

**and**his wife

**,**Hiram Walker

**and**his wife

**,**Joseph Pease

**and**

__R__. H. Valentine.

__Every__smooth submanifold of

__R__

**<**

**sup**> n </

**sup**> has an induced Riemannian metric g:

**the**inner product

**on**each tangent space is

**the**restriction of

**the**inner product

**on**

__R__

**<**

**sup**> n </

**sup**

**>.**

Every and on

__Every__day

**,**when

**the**President took his nap

**,**Rob Roy would stretch out

__on__

**the**window seat near him

**,**like

**a**perfect gentleman

**,**

**and**stare thoughtfully out

**the**window

**,**or he would take

**a**little nap himself.

__Every__man who dabbles in

**the**market

**to**make

**a**little easy money

__on__

**the**side

**and**suffers losses could at

**the**time hardly face his wife who was wondering how her husband could

**be**so dumb.

__Every__few minutes she would awaken for

**a**moment

**to**review things: Stowey

**,**yes

**,**was

__on__his way south

**,**

**and**

**the**two boys were away in school

**,**

**and**nothing was burning

__on__

**the**stove

**,**

**and**Lucretia was coming for dinner

**and**bringing three guests of hers.

__Every__night they all went

**to**Mama

**and**Papa Albright's

**,**

**and**sat

__on__

**the**open front porch

**,**where they could get

**the**breeze.

__Every__few days

**,**in

**the**early morning

**,**as

**the**work progressed

**,**twenty men would appear

**to**push it ahead

**and**

**to**shift

**the**plank foundation that distributed its weight widely

__on__

**the**Rotunda pavement

**,**supported as it is

**by**ancient brick vaulting.

__Every__night when he wanted

**a**drink of water

**,**didn't he practice being fearless

**by**not turning

__on__

**the**bathroom light??

__Every__single instance of altruistic behavior need not always increase inclusive fitness ; altruistic behaviors would have been selected for if such behaviors

__on__average increased inclusive fitness in

**the**ancestral environment.

*

__Every__continuous functor__on__**a**small-complete category which satisfies**the**appropriate solution**set**condition has**a**left-adjoint (**the**Freyd adjoint functor theorem ).__Every__year

**,**

__on__

**the**last Sunday in April

**,**there is an ice fishing competition in

**the**frozen estuarine waters of

**the**Anadyr River's mouth.

__Every__actor who has opened in

**the**role of Pseudolus

__on__Broadway ( Zero Mostel

**,**Phil Silvers

**and**Nathan Lane ) won

**a**Best Actor Tony Award for their performance.

* Revised Code of Washington 9. 12. 010: "

__Every__person who brings__on__his or her own behalf**,**or instigates**,**incites**,**or encourages another**to**bring**,**any false suit at law or in equity in any court of this state**,**with intent thereby**to**distress or harass**a**defendant in**the**suit**,**or who serves or sends any paper or document purporting**to****be**or resembling**a**judicial process**,**that is not in fact**a**judicial process**,**is guilty of**a**misdemeanor ;**and**in case**the**person offending is an attorney**,**he or she may**,**in addition thereto**be**disbarred from practicing law within this state.__Every__year

**,**

**the**European Joint Conferences

__on__Theory

**and**Practice of Software ( ETAPS ) sponsors

**the**International Conference

__on__Compiler Construction ( CC ), with papers from both

**the**academic

**and**industrial sectors.

__Every__Halloween

**,**Dabney House conducts

**the**infamous " Millikan pumpkin-drop experiment " from

**the**top of Millikan Library

**,**

**the**highest point

__on__campus.

__Every__person should

**be**identified uniquely as resident in one place but where they happen

**to**

**be**

__on__census day

**,**their de facto residence

**,**may not

**be**

**the**best place

**to**count them.

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