Page "Axiom of choice" ¶ 58
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## Some Related Sentences

** and lemma
** 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.
** word, lexeme, lemma, lexicon, vocabulary, terminology
** Noether normalization lemma
** Schwarz – Ahlfors – Pick theorem, an extension of the Schwarz lemma for hyperbolic manifolds
** Sperner's lemma
** Schwarz lemma
** Burnside's lemma, a theorem of group theory
** The Lovász local lemma ( proved in 1975, by László Lovász & P. Erdős )
** Algorithmic Lovász local lemma ( proved in 2009, by Robin Moser and Gábor Tardos )
** Krasner's lemma, in number theory
** Hensel's lemma and Henselian rings, named after Kurt

** and Every
** Well-ordering theorem: Every set can be well-ordered.
** Every surjective function has a right inverse.
** Antichain principle: Every partially ordered set has a maximal antichain.
** Every vector space has a basis.
** Every unital ring other than the trivial ring contains a maximal ideal.
** Every infinite game in which is a Borel subset of Baire space is determined.
** Every field has an algebraic closure.
** Every field extension has a transcendence basis.
** Every Tychonoff space has a Stone – Čech compactification.
** 2 ( 2012 ) ( Every hospital, airport and military base has Helipads.
** It Happens Every Spring-Valentine Davies, Shirley Smith
** Every voiced consonant is written with a deep letter similar in shape to the corresponding voiceless consonant which in turn is written with a tall letter.
** The Fugitive Guy: Every so often, Letterman would introduce " Roger Campbell " ( Elliott, wearing an extremely bad toupée ), a new member of the Late Night crew.
** Edwin Hawkins for " Every Man Wants To Be Free " performed by the Edwin Hawkins Singers
** The Police for " Every Breath You Take "
** Luther Vandross and Marcus Miller for " Little Miracles ( Happen Every Day )" performed by Luther Vandross
** L. A. Reid and Babyface for " Every Little Step " performed by Bobby Brown
** 1908 Feb, in Every Where Vol. 21
** A Journey Through Every Stage of Life
** 1664-The Concession and Agreement of the Lords Proprietors of the Province of New Caesarea, or New Jersey, to and With All and Every the Adventurers and All Such as Shall Settle or Plant There
** Sting ( songwriter ) for " Every Breath You Take " performed by The Police
** The Police for " Every Breath You Take "
** Every item entry must be within one level of its predecessor, such that each item must be a sibling or child of the preceding item ( thus, no item can be a grandchild of the preceding item ).

** and non-empty
** For every non-empty set S there is a binary operation defined on S that makes it a group.
** Convex body, a compact convex set with non-empty interior
** It may be non-empty.

** and collection
** The Guoyu, a collection of historical records of numerous states recorded the period from Western Zhou to 453 BCE.
** The Shan Hai Jing, a collection of mythical tales from various locations.
** Garbage collection ( SSD ), in flash memory
** — The collection of drafts, review-comments and other documents relating to the work of the Working Group I of the Assessment Report 4.
** A software suite, or collection of related application or utility software
** Statistical unit, a single data point, or collection of data points grouped as a single entity, on which statistical analysis is performed
** Web 2. 0, a perceived transition of the Web from a collection of Web sites to a full-fledged computing platform serving Web applications
** A collection of short stories that look to mankind's exploration of space, and examine the possibilities that we could face when we decide to take those first fateful steps into the unknown.
** Madonna ( video compilation ), a music video collection
** Watergate tapes, also known as the Nixon tapes, a collection of conversations between U. S. President Richard Nixon and various White House staff members
** Bond: Video Clip Collection, a video collection from the band
** Industry and Occupations Photographs An ongoing and expanding collection devoted to the workers in the Pacific Northwest from 1880s-1940s.
** The Olney Hymns, a collection of hymns written there
** The Sochi Arboretum, which goes back to 1889, possesses the most comprehensive collection of subtropical flora in Russia, including 76 species of pine, 80 species of oak, and 24 species of palm.
** Directly managing the national collection of sites, monuments, archive records and photographs taken into state care since the 1880s.
** " The Ford of Red Hanrahan " ( original to the collection )
** " The Second Weyr " ( original to the collection )
** Application for employment, a form or collection of forms that an individual seeking employment must fill out when seeking employment
** Praecepta ad Filium, a collection of maxims.
** A collection of his speeches.
** Norton Utilities, a collection of software utilities
** ( collection of Suede B-sides )
** Electronic toll collection, aims to eliminate the delay on toll roads by collecting tolls electronically
** Quartic reciprocity, a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x < sup > 4 </ sup > ≡ p ( mod q ) is solvable

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