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Every and finitely
Hilbert's example: " the assertion that either there are only finitely many prime numbers or there are infinitely many " ( quoted in Davis 2000: 97 ); and Brouwer's: " Every mathematical species is either finite or infinite.
# 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 finitely generated group with a recursively enumerable presentation and insoluble word problem is a subgroup of a finitely presented group with insoluble word problem
Every subset of a nowhere dense set is nowhere dense, and the union of finitely many nowhere dense sets is nowhere dense.
Every finitely generated ideal of a Boolean ring is principal ( indeed, ( x, y )=( x + y + xy )).
* Every left ideal I in R is finitely generated, i. e. there exist elements a < sub > 1 </ sub >, ..., a < sub > n </ sub > in I such that I = Ra < sub > 1 </ sub > + ... + Ra < sub > n </ sub >.
Every one of the infinitely many vertices of G can be reached from v < sub > 1 </ sub > with a simple path, and each such path must start with one of the finitely many vertices adjacent to v < sub > 1 </ sub >.
" I can now state the physical version of the Church-Turing principle: ' Every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means.
* Every substructure is the union of its finitely generated substructures ; hence Sub ( A ) is an algebraic lattice.
A finitely-generated abelian group is indecomposable if and only if it is isomorphic to Z or to a factor group of the form for some prime number p and some positive integer n. Every finitely-generated abelian group is a direct sum of ( finitely many ) indecomposable abelian groups.
This is up to isomorphism the only indecomposable module over R. Every left R-module is a direct sum of ( finitely or infinitely many ) copies of this module K < sup > n </ sup >.
Every ( bounded ) convex polytope is the image of a simplex, as every point is a convex combination of the ( finitely many ) vertices.

Every and presented
::: Every Bill which shall have passed the House of Representatives and the Senate, shall, before it become a Law, be presented to the President of the United States ; If he approves he shall sign it, but if not he shall return it, with his Objections to that House in which it shall have originated ...
Every Easter Monday the doge headed a procession from San Marco to the convent of San Zaccaria where the abbess presented him a new camauro crafted by the nuns.
Every year a play ( in the fall ) and a musical ( in the spring ) is presented to the public.
Fans were surprised by the mellower, more mature vibe presented on the record in songs such as the title track and " Every Shining Time You Arrive ".
It is usually presented as sales minus sales discounts, returns, and allowances. Every time a business sells a product or performs a service, it obtains revenue.
Every night of the fair, at 10 pm, a 10-minute fireworks display was presented that could be seen over much of Knoxville.
* Happily Ever After: Fairy Tales for Every Child presented a version of the title story set in New York City featuring Ed Koch as the Happy Prince ( who was the statue of the city's previous mayor ) and Cyndi Lauper as a streetwise pigeon named " Pidge " ( in place of the Swallow ).
* What Every Parent Needs to Know About Standard Singapore English ( RELC and National Library Board ): A series of 3 talks were presented on how parents have an influence on their children's use of Standard English.
Every EIS is required to analyze a No Action Alternative, in addition to the range of alternatives presented for study.
* Every New Year's Eve, a Dance music festival called Together As One is presented, featuring various House, Electro, Techno and Trance DJ's.
Every issue also has a cover CD and a ' Metal In China ' section which promotes and introduces bands on the local Chinese heavy metal scene in which several city scenes are presented and Chinese heavy metal is explained including its function as a ' rebellion of denial ' due to the new sound movement.
Every year there are two main events that give awards to outstanding film trailers: The Key Art Awards, presented by the Hollywood Reporter, and The Golden Trailer Awards.
Every international success was presented as a direct result of the righteousness of the communist rule and ideology.
In 2010, the Museum of Modern Art presented a retrospective of Bontecou's work entitled All Freedom in Every Sense.
Every student must prepare for and pass the Rhetoric Proficiency Exam, which requires passing a three-hour essay that is graded upon coherence of argument, quality of argument, style in which the argument is presented, and grammatical correctness.
He opened a concert for British rock singer Sting at the Coliseo Roberto Clemente, where he presented his hit salsa version of " Every Breath You Take " ( with an amused Sting watching from the sidelines ).
Every year since 1882, Bethany Oratorio Society has presented Handel's Messiah at the college-the longest-running annual performances in North America.
Every temporary owner of the painting was presented, along with their biographical data, including that of the Chairman of the committee, the German banker Hermann J Abs, who had played a key role in the economic design and stabilization of Nazism.
Every order was presented during World War II, except for the controversial 1978 award to Leonid Brezhnev.
The tour started on the top floor and worked downwards, featuring approximately 1, 000 Coca-Cola artifacts presented in chronological order, interactive exhibits such as a replica 1930s soda fountain, video presentations of Coca-Cola advertising over the years, and a 10-minute film called " Every Day of Your Life " about Coke around the world.

Every and group
Every finite simple group is isomorphic to one of the following groups:
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 group G acts on G, i. e. in two natural but essentially different ways:, or.
Every galaxy of sufficient mass in the Local Group has an associated group of globular clusters, and almost every large galaxy surveyed has been found to possess a system of globular clusters.
* Every Lie group is parallelizable, and hence an orientable manifold ( there is a bundle isomorphism between its tangent bundle and the product of itself with the tangent space at the identity )
Every instrumental group ( or section ) has a principal who is generally responsible for leading the group and playing orchestral solos.
* Every closed subgroup of a profinite group is itself profinite ; the topology arising from the profiniteness agrees with the subspace topology.
While he admits the existence of caste-based discrimination, he writes that " Every social group cannot be regarded as a race simply because we want to protect it against prejudice and discrimination ".
Every local group is required to have a seneschal who reports to the kingdom's seneschal.
Every local group is required to have one.
* Every topological group is completely regular.
Every summer the group gathers in Newport, RI for week long dance training, seaside teas, and evenings enjoying the splendors of the Gilded Age.
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 group can be trivially made into a topological group by considering it with the discrete topology ; such groups are called discrete groups.
Every topological group can be viewed as a uniform space in two ways ; the left uniformity turns all left multiplications into uniformly continuous maps while the right uniformity turns all right multiplications into uniformly continuous maps.
Every subgroup of a topological group is itself a topological group when given the subspace topology.
:" Every group is naturally isomorphic to its opposite group "
Every ten years, when the general census of population takes place, each citizen has to declare which linguistic group they belong or want to be aggregated to.

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