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Every completely multiplicative function is a homomorphism of monoids and is completely determined by its restriction to the prime numbers.

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## Some Related Sentences

Every and completely

__Every__now

**and**then an atom

**is**replaced

**by**

**a**

__completely__different atom (

**and**this could be as few as one in

**a**million atoms ).

__Every__family large enough

**to**

__completely__consume

**a**young lamb or wild goat was required

**to**offer one for sacrifice at

**the**Jewish Temple on

**the**afternoon

**of**

**the**14th day

**of**Nisan ,()

**and**eat it that night, which was

**the**15th

**of**Nisan ().

*

__Every__locally compact regular space**is**__completely__regular,**and**therefore every locally compact Hausdorff space**is**Tychonoff**.**__Every__isolated unstable black hole decays rapidly

**to**

**a**stable black hole ;

**and**( modulo quantum fluctuations ) stable black holes can be

__completely__described ( in

**a**Cartesian coordinate system ) at any moment in time

**by**these eleven

**numbers**:

__Every__Ophrys orchid has

**its**own pollinator insect

**and**

**is**

__completely__dependent on this species for

**its**survival

**.**

He has gained

**a**reputation**of**being cursed due**to**several notorious strokes**of**bad luck:__Every__team he was assigned**to**would be__completely__annihilated on their third mission together, save for Sanders himself**.**__Every__hour or so,

**a**10 – 20 minute ' word war '

**is**held in which

**the**entire room falls almost

__completely__silent with concentration, save for

**the**sound

**of**keystrokes

**.**

__Every__day, day-by-day, without fail she would rub herself against

**the**walls, till her clothes became thinner,

**and**thinner till she

__completely__wore it out

**.**

*

__Every__atom in**the**ring must have**a**p orbital, which overlaps with p orbitals on either side (__completely__conjugated ).__Every__time he tried attacking major WWF stars such as The Rock or Kurt Angle, he would run into

**a**wall, statue, milk truck, or just

__completely__miss

**and**trip over his boots

**.**

__Every__variation

**of**

**the**Alpha-Bits line

**is**now made

__completely__with whole grains

**and**three grams

**of**fiber per serving

**.**

__Every__plane B that

**is**

__completely__orthogonalTwo flat subspaces S < sub > 1 </ sub >

**and**S < sub > 2 </ sub >

**of**dimensions M

**and**N

**of**

**a**Euclidean space S

**of**at least M + N dimensions are called

__completely__orthogonal if every line in S1

**is**orthogonal

**to**every line in S2

**.**

Every and multiplicative

__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__nonzero real number has

**a**

__multiplicative__inverse ( i

**.**e

**.**an inverse with respect

**to**multiplication ) given

**by**( or ).

__Every__

**prime**power ( except powers

**of**2 ) has

**a**primitive root ; thus

**the**

__multiplicative__group

**of**integers modulo p < sup > n </ sup > ( or equivalently,

**the**unit group

**of**

**the**ring )

**is**cyclic

**.**

Every and function

__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

**.**

__Every__contraction mapping

**is**Lipschitz continuous

**and**hence uniformly continuous ( for

**a**Lipschitz continuous

__function__,

**the**constant k

**is**no longer necessarily less than 1 ).

__Every__effectively calculable

__function__( effectively decidable predicate )

**is**general recursive italics

__Every__bijective

__function__g has an inverse g < sup >− 1 </ sup >, such that gg < sup >− 1 </ sup > = I ;

__Every__entire

__function__can be represented as

**a**power series that converges uniformly on compact sets

**.**

__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__time another object or customer enters

**the**line

**to**wait, they join

**the**end

**of**

**the**line

**and**represent

**the**“ enqueue ”

__function__

**.**

__Every__type that

**is**

**a**member

**of**

**the**type class defines

**a**

__function__that will extract

**the**data from

**the**string representation

**of**

**the**dumped data

**.**

__Every__output

**of**an encoder can be described

**by**

**its**own transfer

__function__, which

**is**closely related

**to**

**the**generator polynomial

**.**

__Every__continuous

__function__in

**the**

__function__space can be represented as

**a**linear combination

**of**basis functions, just as every vector in

**a**vector space can be represented as

**a**linear combination

**of**basis vectors

**.**

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