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Total order

In mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation ≤ {\displaystyle \leq } on some set X {\displaystyle X} , which satisfies the following for all a , b {\displaystyle a,b} and c {\displaystyle c} in X {\displaystyle X} :

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Overview

Strict and non-strict total orders

Examples

Chains

Further concepts

Orders on the Cartesian product of totally ordered sets

Related structures

Bibliography

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Map overview Semantic statistics

Total order

Nodes119
Edges118
Triples28
Avg. degree1.98
Density0.016807
Components1

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Total order

Top relations

related to Examples · 11
Total order → Any, Any Dedekind-complete, Cartesian, Each, Every, Hence, If, Moreover, Ordered, The, They
related to Orders on the Cartesian product of totally ordered sets · 5
Total order → Cartesian, Here, Lexicographical, There, This
related to Finite total orders · 4
Total order → Either, Hence, In, Thus
is a · 3
Total order → binary relation, totally ordered group.There are only a few nontrivial structures that are, totally ordered set
related to Decidability · 3
Total order → S2S, The, Using
related to Strict and non-strict total orders · 1
Total order → For
related to Sums of orders · 1
Total order → For

Important terminology Word statistics

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Important terminology

set order ordered total totally numbers displaystyle partial orders chain topology real subset leq sets also defined called natural two

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Total orderis abinary relation0.90text
Total orderis atotally ordered set0.90text
Total orderis atotally ordered group.There are only a few nontrivial structures that are0.90text
Total orderrelated to DecidabilityThe0.60section
Total orderrelated to DecidabilityUsing0.60section
Total orderrelated to DecidabilityS2S0.60section
Total orderrelated to ExamplesAny0.60section
Total orderrelated to ExamplesThe0.60section
Total orderrelated to ExamplesIf0.60section
Total orderrelated to ExamplesCartesian0.60section
Total orderrelated to ExamplesHence0.60section
Total orderrelated to ExamplesEach0.60section

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