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单词 OrderingRelation
释义

ordering relation


Let S be a set. An ordering relation is a relation on S such that, for every a,b,cS:

  • Either ab, or ba,

  • If ab and bc, then ac,

  • If ab and ba, then a=b.

Equivalently, an ordering relation is a relation on S which makes the pair (S,) into a totally ordered setMathworldPlanetmath. Warning: In some cases, an author may use the term “ordering relation” to mean a partial orderMathworldPlanetmath instead of a total order.

Given an ordering relation , one can define a relation < by: a<b if ab and ab. The opposite ordering is the relation given by: ab if ba, and the relation > is defined analogously.

Titleordering relation
Canonical nameOrderingRelation
Date of creation2013-03-22 11:52:04
Last modified on2013-03-22 11:52:04
Ownerdjao (24)
Last modified bydjao (24)
Numerical id9
Authordjao (24)
Entry typeDefinition
Classificationmsc 03-00
Classificationmsc 81-00
Classificationmsc 18-00
Classificationmsc 17B37
Classificationmsc 18D10
Classificationmsc 18D35
Classificationmsc 16W30
Related topicTotalOrder
Related topicPartialOrder
Related topicRelation
Definesopposite ordering
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更新时间:2025/5/4 9:32:28