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Every arithmetical set is implicitly arithmetical ; if X is arithmetically defined by φ ( n ) then it is implicitly defined by the formula

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## Some Related Sentences

Every and arithmetical

Every and set

__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.
The restricted principle "

__Every__partially ordered__set__has a maximal totally ordered subset "**is**also equivalent to AC over ZF.
*

__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__continuous map from a compact space to a Hausdorff space**is**closed and proper**(**i. e.,**the**pre-image of a compact__set__**is**compact.__Every__subset A of

**the**vector space

**is**contained within a smallest convex

__set__

**(**called

**the**convex hull of A ), namely

**the**intersection of all convex sets containing A.

__Every__corporation, whether financial or union, as well as every division of

**the**administration, were

__set__up as branches of

**the**party,

**the**CEOs, Union leaders, and division directors being sworn-in as section presidents of

**the**party.

__Every__DNS zone must be assigned a

__set__of authoritative name servers that are installed in NS records in

**the**parent zone, and should be installed

**(**to be authoritative records

**)**as self-referential NS records on

**the**authoritative name servers.

Group actions / representations:

__Every__group G can be considered as a category with a single object whose morphisms are**the**elements of G. A functor from G to Set**is****then**nothing but a group action of G on a particular__set__, i. e. a G-set.
# " Personality " Argument: this argument

**is**based on a quote from Hegel: "__Every__man has**the**right to turn his will upon a thing or make**the**thing an object of his will, that**is**to say, to__set__aside**the**mere thing and recreate**it**as his own ".__Every__atom across this plane has an individual

__set__of emission cones .</ p > < p > Drawing

**the**billions of overlapping cones

**is**impossible, so this

**is**a simplified diagram showing

**the**extents of all

**the**emission cones combined.

*

__Every__preorder can be given a topology,**the**Alexandrov topology**;**and indeed, every preorder on a__set__**is**in one-to-one correspondence with an Alexandrov topology on that__set__.__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 >.

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.

__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 implicitly

Concerning

**the**role of clave in salsa music, Charley Gerard states: “ The clave feeling**is**in**the**music whether or not**the**claves are actually being played .”__Every__ostinato part which spans a cycle of four main beats, has a specific alignment with clave, and expresses**the**rhythmic qualities of clave either explicitly or__implicitly__.__Every__open sentence must have

**(**usually

__implicitly__

**)**a universe of discourse describing which numbers are under consideration as solutions.

__Every__non-leaf node can be thought of as

__implicitly__generating a splitting hyperplane that divides

**the**space into two parts, known as half-spaces.

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