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: Every set has a choice function.

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## Some Related Sentences

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 has

__Every__woman

__has__had the experience of saying no when she meant yes, and saying yes when she meant no

**.**

__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__family of Riviera Presbyterian Church

__has__been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members of the family participate

**.**

__Every__community, if it is alive

__has__

**a**spirit, and that spirit is the center of its unity and identity

**.**

** Tukey's lemma

**:**__Every__non-empty collection of finite character__has__**a**maximal element with respect to inclusion**.**__Every__unit of length

__has__

**a**corresponding unit of area, namely the area of

**a**square with the given side length

**.**

__Every__field

__has__an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of

**choice**

**.**

__Every__ATM cell

__has__an 8-or 12-bit Virtual Path Identifier ( VPI ) and 16-bit Virtual Channel Identifier ( VCI ) pair defined in its header

**.**

Every and choice

__Every__finite-dimensional vector space is isomorphic to its dual space, but this isomorphism relies on an arbitrary

__choice__of isomorphism ( for example, via choosing

**a**basis and then taking the isomorphism sending this basis to the corresponding dual basis ).

__Every__other province had the freedom to regulate the religious question as it wished, although the Union stated every person should be free in the

__choice__of his personal religion and no person should be prosecuted based on his or her religious

__choice__

**.**

__Every__year, the Knights and Setons raise money for

**a**charity of their

__choice__, their most successful fund raiser being the charity ball held every fall

**.**

__Every__conceivable method of applying cutting fluid ( e

**.**g., flooding, spraying, dripping, misting, brushing ) can be used, with the best

__choice__depending on the application and the equipment available

**.**

Many principles that imply the axiom of

__choice__in their general form ( such as "__Every__vector space**has****a**basis ") become provable in weak subsystems of second-order arithmetic when they are restricted**.**__Every__other year, they have

**a**repertoire of student-directed plays, in which students apply to direct

**a**play of their

__choice__

**.**

Dorfl speaks ' With The Beginning Of

__Every__Word Being Capitalized ', as do all golems granted speech, and, like most golems, he is quite literal in his__choice__of words**.**
He wrote, "

__Every__so often**a**director makes an inspiring casting__choice__to not hire**a**real actor for**a**role, but go with an unknown, an amateur**.**__Every__now and then there was

**a**crisis that called for military action, and Lower Fort Garry was the obvious

__choice__for

**a**base of operations

**.**

__Every__effort is made to enable the preferred

__choice__of course requested by students to be timetabled but where an option is not viable in terms of numbers and / or staffing, the Governors reserve the right to withdraw the subject option offer

**.**

**:**

__Every__independent person can acquire

**a**domicile of

__choice__by the jurisdiction of residence and intention of permanent or indefinite residence, but not otherwise

**.**

The first paragraph of article 40, in the current Congolese constitution, states that "

__Every__individual**has**the right to marry the person of their__choice__, of the opposite sex ".__Every__Chinese New Years, the High School students get to spend

**a**week in

**a**location of their

__choice__around the world

**.**

__Every__year, hundreds of thousands of primary school students select to join Alliance High school as their first

__choice__

**.**

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