Matches in DBpedia 2015-10 for { ?s ?p "In mathematics, the Szpilrajn extension theorem, due to Edward Szpilrajn (1930) (later called Edward Marczewski), is one of many examples of the use of the axiom of choice (in the form of Zorn's lemma) to find a maximal set with certain properties.The theorem states that every strict partial order is contained into a total order, where: a strict partial order is a irreflexive and transitive relation a total order is a strict partial order that is also totalIntuitively, the theorem states that a comparison between elements that leaves some pairs incomparable can be extended in such a way every element is either less than or greater than another."@en }
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- Szpilrajn_extension_theorem abstract "In mathematics, the Szpilrajn extension theorem, due to Edward Szpilrajn (1930) (later called Edward Marczewski), is one of many examples of the use of the axiom of choice (in the form of Zorn's lemma) to find a maximal set with certain properties.The theorem states that every strict partial order is contained into a total order, where: a strict partial order is a irreflexive and transitive relation a total order is a strict partial order that is also totalIntuitively, the theorem states that a comparison between elements that leaves some pairs incomparable can be extended in such a way every element is either less than or greater than another.".
- Szpilrajn_extension_theorem comment "In mathematics, the Szpilrajn extension theorem, due to Edward Szpilrajn (1930) (later called Edward Marczewski), is one of many examples of the use of the axiom of choice (in the form of Zorn's lemma) to find a maximal set with certain properties.The theorem states that every strict partial order is contained into a total order, where: a strict partial order is a irreflexive and transitive relation a total order is a strict partial order that is also totalIntuitively, the theorem states that a comparison between elements that leaves some pairs incomparable can be extended in such a way every element is either less than or greater than another.".