- 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. Academic. 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 — 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
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