Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Total_order> ?p ?o }
- 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 requires only 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 wikiPageLength "14181".
- Total_order wikiPageOutDegree "102".
- Total_order wikiPageRevisionID "683618939".
- Total_order wikiPageWikiLink Affinely_extended_real_number_system.
- Total_order wikiPageWikiLink Alphabetical_order.
- Total_order wikiPageWikiLink Antisymmetric_relation.
- Total_order wikiPageWikiLink Asymmetric_relation.
- Total_order wikiPageWikiLink Betweenness_relation.
- Total_order wikiPageWikiLink Bijection.
- Total_order wikiPageWikiLink Binary_relation.
- Total_order wikiPageWikiLink Cardinal_number.
- Total_order wikiPageWikiLink Cartesian_product.
- Total_order wikiPageWikiLink Category:Mathematical_relations.
- Total_order wikiPageWikiLink Category:Order_theory.
- Total_order wikiPageWikiLink Category:Set_theory.
- Total_order wikiPageWikiLink Category_(mathematics).
- Total_order wikiPageWikiLink Compact_space.
- Total_order wikiPageWikiLink Comparability.
- Total_order wikiPageWikiLink Complete_lattice.
- Total_order wikiPageWikiLink Connectedness.
- Total_order wikiPageWikiLink Countable_set.
- Total_order wikiPageWikiLink Counting.
- Total_order wikiPageWikiLink Countryman_line.
- Total_order wikiPageWikiLink Cyclic_order.
- Total_order wikiPageWikiLink Dense_order.
- Total_order wikiPageWikiLink Direct_product.
- Total_order wikiPageWikiLink Distributive_lattice.
- Total_order wikiPageWikiLink Extended_real_number_line.
- Total_order wikiPageWikiLink Group_(mathematics).
- Total_order wikiPageWikiLink Homeomorphism.
- Total_order wikiPageWikiLink If_and_only_if.
- Total_order wikiPageWikiLink Index_set.
- Total_order wikiPageWikiLink Infimum_and_supremum.
- Total_order wikiPageWikiLink Infix_notation.
- Total_order wikiPageWikiLink Initial_segment.
- Total_order wikiPageWikiLink Injective_function.
- Total_order wikiPageWikiLink Integer.
- Total_order wikiPageWikiLink Integers.
- Total_order wikiPageWikiLink Interval_(mathematics).
- Total_order wikiPageWikiLink Isomorphism.
- Total_order wikiPageWikiLink Lattice_(order).
- Total_order wikiPageWikiLink Least_upper_bound.
- Total_order wikiPageWikiLink Lexicographical_order.
- Total_order wikiPageWikiLink Linear_extension.
- Total_order wikiPageWikiLink Linearly_ordered_group.
- Total_order wikiPageWikiLink Logical_disjunction.
- Total_order wikiPageWikiLink Lower_bound.
- Total_order wikiPageWikiLink Map_(mathematics).
- Total_order wikiPageWikiLink Mathematics.
- Total_order wikiPageWikiLink Morphism.
- Total_order wikiPageWikiLink Natural_number.
- Total_order wikiPageWikiLink Natural_numbers.
- Total_order wikiPageWikiLink Normal_space.
- Total_order wikiPageWikiLink Order_isomorphic.
- Total_order wikiPageWikiLink Order_isomorphism.
- Total_order wikiPageWikiLink Order_theory.
- Total_order wikiPageWikiLink Order_topology.
- Total_order wikiPageWikiLink Order_type.
- Total_order wikiPageWikiLink Ordered_field.
- Total_order wikiPageWikiLink Ordered_geometry.
- Total_order wikiPageWikiLink Ordered_vector_space.
- Total_order wikiPageWikiLink Ordinal_number.
- Total_order wikiPageWikiLink Partial_order.
- Total_order wikiPageWikiLink Partially_ordered.
- Total_order wikiPageWikiLink Partially_ordered_set.
- Total_order wikiPageWikiLink Prefix_order.
- Total_order wikiPageWikiLink Product_order.
- Total_order wikiPageWikiLink Rational_number.
- Total_order wikiPageWikiLink Rational_numbers.
- Total_order wikiPageWikiLink Real_number.
- Total_order wikiPageWikiLink Real_numbers.
- Total_order wikiPageWikiLink Reflexive_relation.
- Total_order wikiPageWikiLink Separation_relation.
- Total_order wikiPageWikiLink Set_(mathematics).
- Total_order wikiPageWikiLink Strict_weak_order.
- Total_order wikiPageWikiLink Strict_weak_ordering.
- Total_order wikiPageWikiLink Subcategory.
- Total_order wikiPageWikiLink Subset.
- Total_order wikiPageWikiLink Suslins_problem.
- Total_order wikiPageWikiLink Topology.
- Total_order wikiPageWikiLink Total_relation.
- Total_order wikiPageWikiLink Totally_ordered_group.
- Total_order wikiPageWikiLink Transitive_relation.
- Total_order wikiPageWikiLink Trichotomy_(mathematics).
- Total_order wikiPageWikiLink Tuple.
- Total_order wikiPageWikiLink Unit_interval.
- Total_order wikiPageWikiLink Upper_and_lower_bounds.
- Total_order wikiPageWikiLink Upper_bound.
- Total_order wikiPageWikiLink Upper_set.
- Total_order wikiPageWikiLink Vector_space.
- Total_order wikiPageWikiLink Weak_ordering.
- Total_order wikiPageWikiLink Well-order.
- Total_order wikiPageWikiLink Well_order.
- Total_order wikiPageWikiLink Zorns_lemma.
- Total_order wikiPageWikiLinkText "Chain".
- Total_order wikiPageWikiLinkText "Complete".
- Total_order wikiPageWikiLinkText "Orders on the Cartesian product of totally ordered sets".
- Total_order wikiPageWikiLinkText "Strict total order".