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Every element s, except a possible greatest element, has a unique successor ( next element ), namely the least element of the subset of all elements greater than s. Every subset which has an upper bound has a least upper bound.

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## Some Related Sentences

Every and element

__Every__such

**subset**

**has**

**a**smallest

__element__

**,**so to specify our choice function we can simply say that it maps each set to

**the**

**least**

__element__

**of**that set

**.**

** Zorn's lemma:

__Every__non-empty partially ordered set in**which**every chain**(**i**.**e**.**totally ordered**subset**)**has****an****upper****bound**contains at**least**one maximal__element__**.**
** Tukey's lemma:

__Every__non-empty collection**of**finite character**has****a**maximal__element__with respect to inclusion**.**__Every__lattice

__element__

**of**

**the**structure is in its proper place

**,**whether it is

**a**single atom or

**a**molecular grouping

**.**

__Every__Boolean algebra

**(**A

**,**∧, ∨) gives rise to

**a**ring

**(**A

**,**+, ·) by defining

**a**+ b :=

**(**

**a**∧ ¬ b ) ∨

**(**b ∧ ¬

**a**) =

**(**

**a**∨ b ) ∧ ¬(

**a**∧ b )

**(**this operation is called symmetric difference in

**the**case

**of**sets and XOR in

**the**case

**of**logic ) and

**a**· b :=

**a**∧ b

**.**The zero

__element__

**of**this ring coincides with

**the**0

**of**

**the**Boolean algebra ;

**the**multiplicative identity

__element__

**of**

**the**ring is

**the**1

**of**

**the**Boolean algebra

**.**

__Every__repetition

**of**insertion sort removes

**an**

__element__from

**the**input data

**,**inserting it into

**the**correct position in

**the**already-sorted list

**,**until no input

**elements**remain

**.**

__Every__singleton is

**a**terminal object

**,**with

**the**functions mapping

**all**

**elements**

**of**

**the**source sets to

**the**single target

__element__as morphisms

**.**

*

__Every__non-empty set**of**left ideals**of**R**,**partially ordered by inclusion**,****has****a**maximal__element__with respect to set inclusion**.**__Every__time

**a**pixel on

**a**triangle is rendered

**,**

**the**corresponding texel

**(**or texture

__element__) in

**the**texture must be found

**.**

__Every__non-inner automorphism yields

**a**non-trivial

__element__

**of**Out

**(**G

**),**but different non-inner automorphisms may yield

**the**same

__element__

**of**Out

**(**G ).

Every and s

The work is much more accessible

**than**Sana ’ i ’__s__for instance ; "__Every__line**of****the**Rubaiyat**has**more meaning**than**almost anything you could read in Sufi literature ".__Every__island

**has**one or two short airstrips where Vanair ’

__s__Twin Otter planes land two or three times weekly

**.**

Pirate luminaries such as William Kidd

**,**Henry__Every__**,**John Bowen**,**and Thomas Tew made Antongil Bay and Nosy Boraha**(**St**.**Mary ’__s__Island )**(****a**small island 12 miles off**the**north-east coast**of**Madagascar ) their bases**of**operations**.**
The argument over

**the**quality**of**Fitzgerald ’__s__translation**of****the**Rubaiyat**has****,**according to Dougan**,**diverted attention from**a**fuller understanding**of****the**deeply esoteric message contained in Omar ’__s__actual material – "__Every__line**of****the**Rubaiyat**has**more meaning**than**almost anything you could read in Sufi literature ".__Every__algebraic structure

**has**its own notion

**of**homomorphism

**,**

**namely**any function compatible with

**the**operation

**(**

__s__) defining

**the**structure

**.**

__Every__year

**,**on Father ’

__s__Day weekend

**,**

**the**downtown streets

**of**Logan

**,**Ohio come alive with

**the**celebration

**of**

**the**washboard

**,**as

**a**musical instrument

**.**

__Every__two weeks

**,**

**the**prisoners receive “

**a**special meal

**of**pork broth soup and white-flour steamed buns .” Important Chinese holidays such as New Year ’

__s__

**,**National Day

**,**and

**the**Spring Festival are celebrated with meat dumplings

**,**

**a**special treat in

**an**otherwise meatless diet

**.**

__Every__year since 1979

**,**

**the**world ’

__s__top blacksmiths compete in Calgary

**,**Alberta ; performing their craft in front

**of**thousands

**of**spectators to educate and entertain

**the**public with their skills and abilities

**.**

: Amalek is still alive today .…

__Every__time you experience**a**worry or doubt about how God is running**the**world — that ’__s__Amalek launching**an**attack against your soul**.**
*

__Every__ten years**,**one**of**Flander ’__s__largest floral displays takes place on**the**market square**(**Grote Markt ).__Every__citizen who is thirty-five or older is eligible to be nominated for

**the**presidency ; and must be nominated by either twenty or more representatives from Houses

**of**

**the**Oireachtas

**(**similar to America ’

__s__House

**of**Representatives ) or four administrative counties

**.**

In Histriomastix

**,**Marston satirizes Jonson ’__s__pride through**the**character Chrisoganus ; Jonson responds by satirizing Marstons's wordy style in__Every__Man Out**of**His Humour**,**acted by**the**Lord Chamberlain's Men**.**__Every__kind

**of**material

**has**

**unique**magnetic properties

**,**even those that we do not think

**of**as being “ magnetic .” Different materials below

**the**ground can cause local disturbances in

**the**Earth ’

__s__magnetic field that are detectable with sensitive magnetometers

**.**

Veneman is also co-chair

**of**Mothers Day__Every__Day**,**along with former U**.**S**.**President Bill Clinton ’__s__Health and Human Services Secretary Donna Shalala**.**__Every__motion

**of**

**the**lock is derived from movement

**of**

**the**hands rather

**than**

**elements**beyond

**the**operator ’

__s__control

**,**such as dirt

**,**rust

**,**or memory

**.**

Press reports indicate that Bartlett ’

__s__Political Action Committee is named Because All Responsible Taxpayers Like__Every__Truth Told PAC**,**or BARTLETT PAC for short**.**

Every and except

__Every__member

**of**

**the**future protectionist cabinet then in parliament

**(**

__except__Disraeli ) voted against

**the**measure

**.**

__Every__action specifically intended to prevent procreation is forbidden

**,**

__except__in medically necessary circumstances

**.**

__Every__president since Taft

**,**

__except__for Jimmy Carter

**,**threw out at

**least**one ceremonial first ball or pitch for Opening Day

**,**

**the**All-Star Game

**,**or

**the**World Series

**,**usually with much fanfare

**.**

__Every__S / 360

**(**

__except__for

**the**Model 20

**,**

**which**was not

**a**standard S / 360 ) had

**a**byte-multiplexer channel and 1 or more selector channels

**.**

__Every__twin prime pair

__except__

**(**3

**,**5 ) is

**of**

**the**form

**(**6n − 1

**,**6n + 1 ) for some natural number n

**,**and with

**the**exception

**of**< var > n </ var > = 1

**,**< var > n </ var > must end in 0

**,**2

**,**3

**,**5

**,**7

**,**or 8

**.**

__Every__album

**,**

__except__1969's The Chicago Transit Authority

**,**1978's Hot Streets and 1995's Night and Day: Big-Band

**,**released by Chicago Transit Authority / Chicago

**has**been

**the**band name followed by

**a**Roman numeral or numbered in some other manner

**.**

__Every__state

__except__Nebraska

**has**

**a**bicameral legislature

**,**meaning that

**the**legislature consists

**of**two separate legislative chambers or houses

**.**

__Every__deity and demi-god had been invited

**,**

__except__Eris

**,**

**the**goddess

**of**strife

**(**no one wanted

**a**troublemaker at

**a**wedding ).

__Every__corn-growing country decided to increase tariffs in reaction to this

**,**

__except__Britain and Belgium

**.**

__Every__British North Atlantic route was suspended until 1856

__except__Cunard's Liverpool-Halifax-Boston service

**.**

__Every__evening since 1928

**(**

__except__for

**a**period during

**the**Second World War when Ypres was occupied by Germany

**),**at precisely eight o ' clock

**,**traffic around

**the**imposing arches

**of**

**the**Menin Gate Memorial

**has**been stopped while

**the**Last Post is sounded beneath

**the**Gate by

**the**local fire brigade

**.**

__Every__sequence in principle

**has**

**a**generating function

**of**each type

**(**

__except__that Lambert and Dirichlet series require indices to start at 1 rather

**than**0

**),**but

**the**ease with

**which**they can be handled may differ considerably

**.**

__Every__day had

**the**name

**of**

**an**agricultural plant

**,**

__except__

**the**5th

**(**Quintidi ) and 10th day

**(**Decadi )

**of**every decade

**,**

**which**had

**the**name

**of**

**a**domestic animal

**(**Quintidi ) or

**an**agricultural tool

**(**Decadi ).

__Every__episode

__except__one featured

**a**live performance by

**a**band

**,**including Madness

**,**Motörhead

**,**and The Damned

**.**

__Every__state

**,**

__except__Arkansas and Mississippi

**,**maintains

**a**state FEPA

**(**see EEOC and state FEPA directory ).

__Every__closed 3-manifold

**has**

**a**prime decomposition: this means it is

**the**connected sum

**of**prime three-manifolds

**(**this decomposition is essentially

**unique**

__except__for

**a**small problem in

**the**case

**of**non-orientable manifolds ).

__Every__day had

**the**name

**of**

**an**agricultural plant

**,**

__except__

**the**5th

**(**Quintidi ) and 10th day

**(**Decadi )

**of**every decade

**,**

**which**had

**the**name

**of**

**a**domestic animal or

**an**agricultural tool

**,**respectively

**.**

__Every__province in Canada

__except__Alberta

**has**either

**a**Provincial Sales Tax

**(**PST ) or

**the**Harmonized Sales Tax

**(**HST

**),**

**which**is

**a**single

**,**blended combination

**of**

**the**GST and PST

**.**

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