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- Total_order abstract "In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation (here denoted by infix ≤) on some set X which is transitive, antisymmetric, and total. A set paired with a total order is called a totally ordered set, a linearly ordered set, a simply ordered set, or a chain.If X is totally ordered under ≤, then the following statements hold for all a, b and c in X: If a ≤ b and b ≤ a then a = b (antisymmetry); If a ≤ b and b ≤ c then a ≤ c (transitivity); a ≤ b or b ≤ a (totality).Antisymmetry eliminates uncertain cases when both a precedes b and b precedes a. A relation having the property of "totality" means that any pair of elements in the set of the relation are comparable under the relation. This also means that the set can be diagrammed as a line of elements, giving it the name linear. Totality also implies reflexivity, i.e., a ≤ a. Therefore, a total order is also a partial order. The partial order has a weaker form of the third condition (it only requires reflexivity, not totality). An extension of a given partial order to a total order is called a linear extension of that partial order.".
- Total_order wikiPageID "30330".
- Total_order wikiPageRevisionID "591526095".
- Total_order hasPhotoCollection Total_order.
- Total_order subject Category:Mathematical_relations.
- Total_order subject Category:Order_theory.
- Total_order subject Category:Set_theory.
- Total_order comment "In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation (here denoted by infix ≤) on some set X which is transitive, antisymmetric, and total.".
- Total_order label "Orden total".
- Total_order label "Ordine totale".
- Total_order label "Ordre total".
- Total_order label "Porządek liniowy".
- Total_order label "Relação de ordem".
- Total_order label "Total order".
- Total_order label "Totale orde".
- Total_order label "Линейно упорядоченное множество".
- Total_order label "ترتيب كلي".
- Total_order label "全序关系".
- Total_order label "全順序".
- Total_order sameAs Lineární_uspořádání.
- Total_order sameAs Orden_total.
- Total_order sameAs Ordre_total.
- Total_order sameAs Ordine_totale.
- Total_order sameAs 全順序.
- Total_order sameAs 완전순서.
- Total_order sameAs Totale_orde.
- Total_order sameAs Porządek_liniowy.
- Total_order sameAs Relação_de_ordem.
- Total_order sameAs m.07gj6.
- Total_order sameAs Q369377.
- Total_order sameAs Q369377.
- Total_order wasDerivedFrom Total_order?oldid=591526095.
- Total_order isPrimaryTopicOf Total_order.