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Page "Completeness (order theory)" ¶ 28
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Every and domain
Every principal ideal domain is a unique factorization domain ( UFD ).
# Every principal ideal domain is Noetherian.
# Every finitely generated ideal of A is principal ( i. e., A is a Bézout domain ) and A satisfies the ascending chain condition on principal ideals.
Every domain name appears in a zone served by one or more authoritative name servers.
Every domain name ends in a top-level or first-level domain label.
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 function symbol has an associated arity, indicating the number of elements in the domain mapped onto each element of range.
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 ).
The Highland MP and antiquarian, Charles Fraser-Mackintosh, comments on late eighteenth century evictions in the area of Kingussie, in his second series of " Antiquarian Notes " ( Inverness 1897, pp 369 et seq, public domain ) as follows: " Mr James MacPherson of Ossianic fame, who acquired Phoiness, Etterish, and Invernahaven, began this wretched business and did it so thoroughly that not much remained for his successors ....... Every place James MacPherson acquired was cleared, and he also had a craze for changing and obliterating the old names ......
Every field of either type can be realized as the field of fractions of a Dedekind domain in which every non-zero ideal is of finite index.
* Every constant function whose domain and codomain are the same is idempotent.
* Every Jacobi-like polynomial sequence can have its domain shifted and / or scaled so that its interval of orthogonality is, and has Q
* Every Laguerre-like polynomial sequence can have its domain shifted, scaled, and / or reflected so that its interval of orthogonality is, and has Q =
* Every Hermite-like polynomial sequence can have its domain shifted and / or scaled so that its interval of orthogonality is, and has Q
Every village, town and city can build a Wizard Tower, and the Wizard only has to be inside one Wizard Tower, the other towers will also increase his domain.
Every domain that supports the SMTP protocol for electronic mail is required by RFC 5321 and, as early as 1982, by RFC 822, to have the postmaster address.
Every domain may have a different timeline, adjusting events based on the domain's current time.
Every incoming email has an IP address that is difficult to forge, a bunch of domain names in the email headers, and a few more in the commands from the sender's SMTP server.
* Every concave function that is nonnegative on its domain is log-concave.
Every record has a unique identifier, which indicates the domain name of the original repository where the record was created.

Every and D
Every song they wrote was written with an eye toward giving it " deep hidden meaning " or D. H. M.
Also among the early 32 members were syndicated panel cartoonists Dave Breger ( Mister Breger ), George Clark ( The Neighbors ), Bob Dunn ( Just the Type ) and Jimmy Hatlo ( They'll Do It Every Time ); freelance magazine cartoonists Abner Dean and Mischa Richter, editorial cartoonists Rube Goldberg ( New York Sun ), Burris Jenkins ( New York Journal American ), C. D. Batchelor ( Daily News ) and Richard Q. Yardley ( The Baltimore Sun ); sports cartoonist Lou Hanlon ; illustrator Russell Patterson and comic book artists Joe Shuster and Joe Musial.
Every year there is a volunteer of the year award and also the ' John D Hammer ' trophy for the ' Junior volunteer of the year '.
Every adjunction 〈 F, G, ε, η 〉 gives rise to an associated monad 〈 T, η, μ 〉 in the category D. The functor
Every meromorphic function on D can be expressed as the ratio between two holomorphic functions ( with the denominator not constant 0 ) defined on D: any pole must coincide with a zero of the denominator.
Every year at the International Astronautical Congress, three prestigious awards are given out: the Allan D. Emil Memorial Award, the Franck J. Malina Astronautics Medal and the Luigi G. Napolitano Award.
Every universal cover p: D → X is regular, with deck transformation group being isomorphic to the fundamental group.
The deputy director of the North Central Association of Colleges and Schools ( NCACS ), Steven D. Crow, says " Every move the university's made has been monitored " and MIU's library, faculty, academic mission and classroom space have been deemed appropriate.
Every fall, FRC Action ( the political action group affiliated with FRC ) holds an annual summit composed for conservative Christian activists and evangelical voters in Washington, D. C.
Every functor F: D → E induces a functor F < sup > C </ sup >: D < sup > C </ sup > → E < sup > C </ sup > ( by composition with F ).
:# Every element of D is the least upper bound of a countable increasing sequence of isolated elements.
* Why Does Nearly Every Culture Have a Tradition of a Global Flood John D. Morris, Ph. D.
Every member of the group has an alias by which he is known, the band's founding members adopting the personas Larry Love ( Rob Spragg ) and The Very Reverend Dr. D. Wayne Love ( Jake Black ).
* Every audience member had his or her own A / B / C / D keypad.
After gaining a minor role in Annie Hall in 1977, D ' Angelo appeared in a string of hit movies in the late 1970s, including Every Which Way But Loose, Hair, and Coal Miner's Daughter, the latter earning her a Golden Globe nomination for Best Supporting Actress and a Country Music Association award for Album of the Year.
Although the organization is secretive, it holds one regular public event each year, the National Prayer Breakfast held in Washington, D. C. Every sitting United States president since President Dwight D. Eisenhower, up to President Barack Obama, has participated in at least one National Prayer Breakfast during his term.

Every and can
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.
Every information exchange between living organisms — i. e. transmission of signals that involve a living sender and receiver can be considered a form of communication ; and even primitive creatures such as corals are competent to communicate.
Every context-sensitive grammar which does not generate the empty string can be transformed into an equivalent one in Kuroda normal form.
* Every regular language is context-free because it can be described by a context-free grammar.
Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed into an equivalent one which is in Chomsky normal form.
Every real number has a ( possibly infinite ) decimal representation ; i. e., it can be written as
Every module over a division ring has a basis ; linear maps between finite-dimensional modules over a division ring can be described by matrices, and the Gaussian elimination algorithm remains applicable.
Every entire function can be represented as a power series that converges uniformly on compact sets.
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.
Every positive integer n > 1 can be represented in exactly one way as a product of prime powers:
Every sequence can, thus, be read in three reading frames, each of which will produce a different amino acid sequence ( in the given example, Gly-Lys-Pro, Gly-Asn, or Glu-Thr, respectively ).
Every hyperbola is congruent to the origin-centered East-West opening hyperbola sharing its same eccentricity ε ( its shape, or degree of " spread "), and is also congruent to the origin-centered North-South opening hyperbola with identical eccentricity ε — that is, it can be rotated so that it opens in the desired direction and can be translated ( rigidly moved in the plane ) so that it is centered at the origin.
Every holomorphic function can be separated into its real and imaginary parts, and each of these is a solution of Laplace's equation on R < sup > 2 </ sup >.
Every species can be given a unique ( and, one hopes, stable ) name, as compared with common names that are often neither unique nor consistent from place to place and language to language.
Every vector v in determines a linear map from R to taking 1 to v, which can be thought of as a Lie algebra homomorphism.
Every morpheme can be classified as either free or bound.
Every use of modus tollens can be converted to a use of modus ponens and one use of transposition to the premise which is a material implication.
Every document window is an object with which the user can work.
Every adult, healthy, sane Muslim who has the financial and physical capacity to travel to Mecca and can make arrangements for the care of his / her dependants during the trip, must perform the Hajj once in a lifetime.
Every ordered field can be embedded into the surreal numbers.
* Every finite topological space gives rise to a preorder on its points, in which x ≤ y if and only if x belongs to every neighborhood of y, and every finite preorder can be formed as the specialization preorder of a topological space in this way.
* 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 >.

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