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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.

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## Some Related Sentences

Every and measurable

__Every__

__measurable__entity maps into

**a**

**cardinal**

**function**but not

**every**

**cardinal**

**function**

**is**the result of the mapping of

**a**

__measurable__entity

**.**

*

__Every__set of reals**in**L ( R )**is**Lebesgue__measurable__(**in**fact**,**universally__measurable__) and has the property of Baire and the perfect set property**.**

Every and cardinal

__Every__strongly inaccessible

__cardinal__

**is**also weakly inaccessible

**,**as

**every**strong limit

__cardinal__

**is**also

**a**weak limit

__cardinal__

**.**

__Every__strong limit

__cardinal__

**is**also

**a**weak limit

__cardinal__

**,**

**because**

**κ**

**<**

**sup**>+</

**sup**

**>**≤ 2

**<**

**sup**

**>**

**κ**

**</**

**sup**

**>**for

**every**

__cardinal__

**κ**

**,**where

**κ**

**<**

**sup**>+</

**sup**

**>**denotes the successor

__cardinal__of

**κ**

**.**

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 because

__Every__pitch

**in**the game brought forth

**a**howl

**from**the enraptured audience and

**every**fly ball the visitors dropped ( and

__because__their right fielder was still

**a**little fuzzy

**from**drink

**,**they dropped many ) called forth yelps of derision

**.**

__Every__Hilbert space X

**is**

**a**Banach space

__because__

**,**by definition

**,**

**a**Hilbert space

**is**complete with respect

**to**the norm associated with its inner product

**,**where

**a**norm and an inner product are said

**to**be associated if for all x ∈ X

**.**

__Every__week before June 19

**,**the strip focuses on Garfield's birthday

**,**which he dreads

__because__of his fear of getting older

**.**

A Girl

**in**__Every__Port**is**considered by film scholars**to**be the most important film of Hawks's silent career__because__it**is**his first film**to**introduce many of the Hawksian themes and characters**that**would continue until his final films**.**
These languages all use special-purpose knowledge engineering

__because__as stated by Tom Gruber**,**"__Every__ontology**is****a**treaty-a social agreement among people with common motive**in**sharing**.**
While he admits the existence of caste-based discrimination

**,**he writes**that**"__Every__social group cannot be regarded as**a**race simply__because__we want**to**protect it against prejudice and discrimination ".
The philosophe Condillac observed

**in**1782**that**"__Every__science requires**a**special language__because__**every**science has its own ideas**.**__Every__ball

**that**goes into the center gate results

**in**one spin of the slot machine

**,**but there

**is**

**a**limit on the number of spins at one time

__because__of the possibility of balls passing through the center gate while

**a**spin

**is**still

**in**progress

**.**

" In an interesting meditation on what he viewed as the harm which would result if Christian ideals were abandoned

**in**Belgium**,**he said: "__Every__time society has distanced itself**from**the Gospel**,**which preached humility**,**fraternity**,**and peace**,**the people have been unhappy**,**__because__the pagan civilization of ancient Rome**,**which they wanted**to**replace it with**,****is**based only on pride and the abuse of force " ( Commemorative speech for the war dead of the Battle of the Yser**,**given by Dom Marie-Albert**,**Abbot of Orval Abbey**,**Belgium**,****in**1936 ).__Every__polynomial

**in**can be factorized into polynomials

**that**are irreducible over F

**.**This factorization

**is**unique up

**to**permutation of the factors and the multiplication of the factors by nonzero constants

**from**F (

__because__the ring of polynomials over

**a**field

**is**

**a**unique factorization domain whose units are the nonzero constant polynomials ).

__Every__finite-dimensional normed space

**is**reflexive

**,**simply

__because__

**in**this case

**,**the space

**,**its dual and bidual all have the same linear dimension

**,**hence the linear injection J

**from**the definition

**is**bijective

**,**by the rank-nullity theorem

**.**

__Every__finite-dimensional Hausdorff topological vector space

**is**reflexive

**,**

__because__J

**is**bijective by linear algebra

**,**and

__because__there

**is**

**a**unique Hausdorff vector space topology on

**a**finite dimensional vector space

**.**

#

__Every__man shall be called fairly**in**turn by the list on board of prizes**,**__because__over and above their proper share**,**they are allowed**a**shift of clothes**.**__Every__funny car has ballistic blankets covering the supercharger

__because__this part of the engine

**is**prone

**to**explosion

**.**

Harrison had

**a**number of " trademark " phrases**,**such as " Morning**,**Mom ", "__Every__brand new day should be opened like**a**precious gift ", " Stay well**,**stay happy**,**stay right here " and " Harry Harrison wishing you the best ...__because__that's exactly what you deserve !” Also**,**on the last day of**every**year**,**Harrison would bring his four children**to**work with him and at the end of his shift**,**he would join them**in**giving listeners New Year's wishes**.**__Every__weekends

**,**lots of people are fond of going around these department stores

**,**

__because__their location

**is**usually easy

**to**visit

**.**

__Every__Russian had heard of Smirnoff vodka and everyone thought it must be the best

__because__they weren't allowed

**to**have it

**.**

__Every__morning

**,**she visited her husband

**in**her nightgown

**,**which was seen as shocking

**,**

__because__her husband usually conferred with members of the council of state

**in**his bed chamber at

**that**time

**.**

__Every__cognition implies necessarily

**a**judgment

**,**but not

**every**judgment

**is**necessarily cognition

**,**

__because__there are also judgments

**that**are not true

**.**

__Every__major political or religious event involved bloodletting

__because__it provided

**a**medium by which the gods could be called upon

**to**witness and actually participate

**in**the ceremony

**.**

__Every__year

**,**on the second Sunday of May

**,**Tzu Chi treats this as

**a**3-in-1 celebration day

__because__on this day

**,**Buddha's Birthday

**,**Mother's Day and Tzu Chi day

**is**being celebrated

**.**

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