Page "Axiom of regularity" ¶ 3
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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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