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- Weak_ordering abstract "In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other. Weak orders are a generalization of totally ordered sets (rankings without ties) and are in turn generalized by partially ordered sets and preorders.There are several common ways of formalizing weak orderings, that are different from each other but cryptomorphic (interconvertable with no loss of information): they may be axiomatized as strict weak orderings (partially ordered sets in which incomparability is a transitive relation), as total preorders (transitive binary relations in which at least one of the two possible relations exists between every pair of elements), or as ordered partitions (partitions of the elements into disjoint subsets, together with a total order on the subsets). In many cases another representation called a preferential arrangement based on a utility function is also possible.Weak orderings are counted by the ordered Bell numbers. They are used in computer science as part of partition refinement algorithms, and in the C++ Standard Library.".
- Weak_ordering thumbnail 13-Weak-Orders.svg?width=300.
- Weak_ordering wikiPageID "828131".
- Weak_ordering wikiPageRevisionID "589536582".
- Weak_ordering hasPhotoCollection Weak_ordering.
- Weak_ordering subject Category:Integer_sequences.
- Weak_ordering subject Category:Mathematical_relations.
- Weak_ordering subject Category:Order_theory.
- Weak_ordering comment "In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other.".
- Weak_ordering label "Preorden total".
- Weak_ordering label "Strenge schwache Ordnung".
- Weak_ordering label "Weak ordering".
- Weak_ordering sameAs Strenge_schwache_Ordnung.
- Weak_ordering sameAs Preorden_total.
- Weak_ordering sameAs m.03ff35.
- Weak_ordering sameAs Q1414271.
- Weak_ordering sameAs Q1414271.
- Weak_ordering wasDerivedFrom Weak_ordering?oldid=589536582.
- Weak_ordering depiction 13-Weak-Orders.svg.
- Weak_ordering isPrimaryTopicOf Weak_ordering.
