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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 totally ordered
set is directed
.
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
.

# ( Accessibility Property )
Every non-empty feasible
set X
contains an element x such that X
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 set has a choice 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.

** Well-ordering theorem
: Every set can be well-ordered
.

The restricted principle "
Every partially ordered
set has a maximal totally ordered subset "
is also equivalent to AC over ZF
.

** Antichain principle
: Every partially ordered
set has a maximal antichain
.

*
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 cofinal subset of a partially ordered
set must contain all maximal elements of that
set.
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 singleton
set
Every processor or processor family has its own machine code instruction
set.
Every set is a class, no matter
which foundation
is chosen
.

*
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 unital ring other than the trivial ring
contains a maximal ideal
.
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
.
Every organic compound
contains at least one atom of carbon
.
Every ordered field
contains an ordered subfield that
is isomorphic to the rational 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 altar in every Orthodox church
contains relics, usually of martyrs
.
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 PostScript printer
contains a RIP in its firmware
.

*
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 bag of blood ( 450 – 500 ml )
contains 200 – 250 milligrams of iron
.
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
.
Every prostaglandin
contains 20 carbon atoms, including a 5-carbon ring
.
Every device
contains at least one swap chain
.
Every living organism
contains DNA, RNA, and proteins
.
Every game in the Mario Party series
contains 50 to 80 mini-games of a few different types
.

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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