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# 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 by one of the relationships “less than,” “equal to,” or “greater than” has an upper bound in S, then S contains at least one element for which there is no greater element in S

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/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 element.
[1945-50; after Max August Zorn (born 1906), German mathematician]

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Zorn's lemma «zawrnz»,
Mathematics. the principle that if a set is partially ordered and each completely ordered subset has an upper bound, then the set has at least one element greater than any other element in the set.
[< Max A. Zorn, born 1906, a German mathematician]

Useful english dictionary. 2012.

### Look at other dictionaries:

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