Zorn's lemma

Zorn's lemma
A proposition in set theory equivalent to the axiom of choice . Call a set A a chain if for any two members B and C, either B is a subset of C or C is a subset of B. Now consider a set D with the properties that for every chain E that is a subset of D, the union of E is a member of D. The lemma states that D contains a member that is maximal, i.e. which is not a subset of any other set in D.

Philosophy dictionary. . 2011.

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  • Zorn's lemma — Zorn s lemma, also known as the Kuratowski Zorn lemma, is a proposition of set theory that states:Every partially ordered set in which every chain (i.e. totally ordered subset) has an upper bound contains at least one maximal element.It is named… …   Wikipedia

  • Zorn's lemma — /zawrnz/, Math. a theorem of set theory that if every totally ordered subset of a nonempty partially ordered set has an upper bound, then there is an element in the set such that the set contains no element greater than the specified given… …   Universalium

  • zorn's lemma — ˈzȯ(ə)rnz , ˈtsȯ noun Usage: usually capitalized Z Etymology: after Max August Zorn died 1993 American (German born) mathematician : a lemma in set theory: if S is partially ordered and if each subset for which every pair of elements is related …   Useful english dictionary

  • Zorn's Lemma (film) — Infobox Film name = Zorn s Lemma caption = director = Hollis Frampton producer = writer = starring = music = cinematography = editing = distributor = released = runtime = 60 min. country = flagicon|USA USA awards = language = English budget =… …   Wikipedia

  • Zorn's lemma — noun Etymology: Max August Zorn died 1993 German mathematician Date: circa 1950 a lemma in set theory: if a set S is partially ordered and if each subset for which every pair of elements is related by exactly one of the relationships “less than,” …   New Collegiate Dictionary

  • Zorn's lemma — noun A proposition of set theory stating that every partially ordered set, in which every chain (i.e. totally ordered subset) has an upper bound, contains at least one maximal element …   Wiktionary

  • Zorn's Law — * Zorn s law is a maxim coined by Chicago Tribune columnist Eric Zorn as a Wikipedia prank. * Zorn s lemma is a proposition used in many areas of theoretical mathematics …   Wikipedia

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  • Lemma von Zorn — Das Lemma von Zorn, auch bekannt als Lemma von Kuratowski Zorn, ist ein Theorem der Mengenlehre, genauer gesagt, der Zermelo Fraenkel Mengenlehre, die das Auswahlaxiom einbezieht. Es ist benannt nach dem deutsch amerikanischen Mathematiker Max… …   Deutsch Wikipedia

  • Lemma von Teichmüller-Tukey — Das Lemma von Teichmüller Tukey (nach Oswald Teichmüller und John W. Tukey), manchmal auch nur Lemma von Tukey genannt, ist ein Satz aus der Mengenlehre. Es ist im Rahmen der Mengenlehre auf Grundlage der ZF Axiome äquivalent zum Auswahlaxiom und …   Deutsch Wikipedia

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