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Some Related Sentences
Every and ordered

** 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
.

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

*
Every cofinal subset of a partially
ordered set must contain all maximal elements of
that set
.
Every non-empty totally
ordered set
is directed
.
Every subfield of
an ordered field is also
an ordered field in
the inherited order
.
Every ordered field is a formally real
field.
Every subfield of
an ordered field is also
an ordered field ( inheriting
the induced ordering ).
Every ordered field can be embedded into
the surreal
numbers.
Every ordered field is a formally real
field, i
. e., 0 cannot be written as a sum of nonzero squares
.

*
Every totally
ordered set with
the order topology
is Tychonoff
.

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

*
Every totally
ordered set
that is a bounded lattice
is also a Heyting algebra, where
is equal
to when, and 1 otherwise
.

*
Every totally
ordered set
is a distributive lattice with max as join and min as meet
.
Every relatively atomic partially
ordered set with a least element
is atomic
.
Every ordered basis lives in one equivalence class or another
.
Every time she entered, song typical of
the Brazilian northeast would play, stopping only when
ordered by Cirene herself
.
Every partially
ordered set
is cofinal in itself
.
Every and field

**
Every field has
an algebraic closure
.

**
Every field extension has a transcendence basis
.
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 field is, of course, one-dimensional over its center
.
Every time
an MTA receives
an email message, it adds a < tt > Received </ tt > trace header
field to the top of
the header of
the message, thereby building a sequential record of MTAs handling
the message
.
Every instruction consists of a 9-bit opcode, a 4-bit register code, and a 23-bit effective address
field, which consists in turn of a 1-bit indirect bit, a 4-bit register code, and
an 18-bit offset
.
Every field theory of particle physics
is based on certain symmetries of nature whose existence
is deduced from observations
.
Every planetary body ( including
the Earth )
is surrounded by its own gravitational
field, which exerts
an attractive force on all objects
.
Every prime ideal P in a Boolean ring R
is maximal:
the quotient ring R / P
is an integral domain and also a Boolean ring, so it
is isomorphic to the field F < sub > 2 </ sub >, which shows
the maximality of P
. Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings
.
Every local
field is isomorphic ( as a topological
field )
to one of
the following:
Every year,
the British Political Studies Association awards
the Walter Bagehot Prize for
the best dissertation in
the field of government and public administration
.
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 quadratic form q in n variables over a
field of characteristic not equal
to 2
is equivalent
to a diagonal form
Every kind of material has unique magnetic properties, even those
that we do not think of as being “ magnetic .” Different materials below
the ground can cause local disturbances in
the Earth ’ s magnetic
field that are detectable with sensitive magnetometers
.
Every and contains

**
Every unital ring other than
the trivial ring
contains a maximal ideal
.

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

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
.
0.368 seconds.