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* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

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## Some Related Sentences

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

**.**

__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 >.

*****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 is

__Every__legislator from Brasstown Bald to Folkston

__is__going to have his every vote subjected to

**the**closest scrutiny as

**a**test of his political allegiances, not his convictions

**.**

__Every__detail

**in**his interpretation

**has**been beautifully thought out,

**and**of these I would especially cite

**the**delicious laendler touch

**the**pianist brings to

**the**fifth variation

**(**an obvious indication that he

__is__playing with Viennese musicians

**)**,

**and**

**the**gossamer shading throughout

**.**

__Every__taxpayer

__is__well aware of

**the**vast size of our annual defense budget

**and**most of our readers also realize that

**a**large portion of these expenditures go for military electronics

**.**

__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__dream,

**and**this

__is__true of

**a**mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought,

__is__

**a**psychic phenomenon for which no explanation

__is__available

**.**

__Every__library borrower, or at least those whose taste goes beyond

**the**five-cent fiction rentals, knows what it

__is__to hear

**the**librarian say apologetically, `` I'm sorry, but we don't have that book

**.**

__Every__community, if it

__is__alive

**has**

**a**spirit,

**and**that spirit

__is__

**the**center of its unity

**and**identity

**.**

The restricted principle "

__Every__partially ordered set**has****a**maximal totally ordered subset "__is__also equivalent to AC over ZF**.**__Every__natural-born citizen of

**a**foreign state who

__is__also an American citizen

**and**every natural-born American citizen who

__is__

**a**citizen of

**a**foreign land owes

**a**double allegiance, one to

**the**United States,

**and**one to his homeland

**(**

**in**

**the**event of an immigrant becoming

**a**citizen of

**the**US ), or to his adopted land

**(**

**in**

**the**event of an emigrant natural born citizen of

**the**US becoming

**a**citizen of another nation ).

__Every__line of written text

__is__

**a**mere reflection of references from any of

**a**multitude of traditions, or, as Barthes puts it, "

**the**text

__is__

**a**tissue of quotations drawn from

**the**innumerable centres of culture "; it

__is__never original

**.**

__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__lattice element of

**the**structure

__is__

**in**its proper place, whether it

__is__

**a**single atom or

**a**molecular grouping

**.**

Every and M

__Every__smooth

**(**or differentiable

**)**map φ:

__M__→ N between smooth

**(**or differentiable

**)**manifolds induces natural linear maps between

**the**corresponding tangent spaces:

__Every__measurable cardinal κ

**is**

**a**0-huge cardinal because < sup > κ </ sup >

__M__⊂

__M__, that

**is**, every function from κ to

__M__

**is**

**in**

__M__

**.**Consequently, V < sub > κ + 1 </ sub >⊂

__M__

**.**

:

__Every__countable theory which**is**satisfiable**in****a**model__M__,**is**satisfiable**in****a**countable substructure of__M__**.*******Siegal,

__M__., Cornell Feline Health Center

**(**Editors

**)**

**(**1989

**)**The Cornell Book of Cats: A Comprehensive Medical Reference for

__Every__Cat

**and**Kitten

**.**

__Every__year about 5000 applications are received, out of which about 300 students

**(**around 150

**in**each year

**)**are enrolled

**in**

**the**2 year full time

__M__

**.**Tech

**.**

__Every__hyperkähler manifold

__M__

**has**

**a**2-sphere of complex structures

**(**i

**.**e

**.**integrable almost complex structures

**)**with respect to which

**the**metric

**is**Kähler

**.**

__Every__finite-length module

__M__

**has**

**a**composition series,

**and**

**the**

**length**of every such composition series

**is**equal to

**the**

**length**of

__M__

**.**

*****

__Every__direct summand of

__M__

**is**pure

**in**

__M__

**.**Consequently, every subspace of

**a**vector space over

**a**field

**is**pure

**.**

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