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: Every non-empty set A contains an element B which is disjoint from A.

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## Some Related Sentences

Every and non-empty

** 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****.**
** Tukey's lemma

**:**__Every____non-empty__collection of finite character has a maximal**element**with respect to inclusion**.**__Every__

__non-empty__intersection of a 3-sphere with a three-dimensional hyperplane

**is**a 2-sphere ( unless the hyperplane

**is**tangent to the 3-sphere, in

**which**case the intersection

**is**a single point ).

*

__Every____non-empty__**set**of left ideals of R, partially ordered by inclusion, has a maximal**element**with respect to**set**inclusion**.**
*

__Every____non-empty__Baire space**is**of second category in itself, and every intersection of countably many dense open subsets of X**is**__non-empty__, but the converse of neither of these**is**true, as**is**shown by the topological**disjoint**sum of the rationals and the unit interval 1**.**__Every__

__non-empty__file must have at least one fork, and depending on the file system, a file may have one or more other associated forks,

**which**in turn may contain primary data integral to the file, or just metadata

**.**

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__

**.**

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 contains

__Every__computer

__contains__

**an**internal clock that regulates the rate at

**which**instructions are executed and synchronizes all the various computer components

**.**

Cantor points out that his constructions prove more — namely, they provide a new proof of Liouville's theorem

**:**__Every__interval__contains__infinitely many transcendental numbers**.**
The revised edition of Robyn was released in the UK in April 2007, and

__contains__two new tracks —" With__Every__Heartbeat " ( a collaboration with Kleerup ) and " Cobrastyle " ( a cover of a 2006 single by Swedish rockers Teddybears )— alongside slightly altered versions of two of the original songs**.**
#

__Every__simple path**from**a given node to any of its descendant leaves__contains__the same number of black nodes**.**__Every__synset

__contains__a group of synonymous words or collocations ( a collocation

**is**a sequence of words that go together to form a specific meaning, such as " car pool "); different senses of a word are in different synsets

**.**

*

__Every__connected graph G admits a spanning tree,**which****is**a tree that__contains__every vertex of G and whose edges are edges of G**.**__Every__one has higher glucose levels for one or two hours after eating food

**which**

__contains__some types of carbohydrates

**.**

__Every__temple of The Church of Jesus Christ of Latter-day Saints ( LDS Church )

__contains__a baptismal font on twelve oxen that

**is**modeled after the molten sea

**.**

__Every__issue of GAMES Magazine

__contains__a large crossword with a double clue list, under the title The World's Most Ornery Crossword ; both lists are straight and arrive at the same solution, but one list

**is**significantly more challenging than the other

**.**

__Every__gap sequence that

__contains__1 yields a correct sort ; however, the properties of thus obtained versions of Shellsort may be very different

**.**

The offset part of the logical address

__contains__**an**offset inside the segment, i**.**e**.**the physical address can be calculated as ( if the address line A20**is**enabled ), respectively ( segment_part × 16 + offset ) mod 2 < sup > 20 </ sup > ( if A20**is**off )__Every__segment has a size of 2 < sup > 16 </ sup > bytes**.**__Every__chapter

__contains__a comprehensive compilation all of the published examples of the reaction organized in tables according to the structure of the starting material

**.**

__Every__Riemann surface

**is**a two-dimensional real analytic manifold ( i

**.**e., a surface ), but it

__contains__more structure ( specifically a complex structure )

**which**

**is**needed for the unambiguous definition of holomorphic functions

**.**

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