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单词 LawOfTrichotomy
释义

law of trichotomy


The law of trichotomy for a binary relationMathworldPlanetmath R on a set S is the property that

  • for all x,yS, exactly one of the following holds: xRy or yRx or x=y.

A binary relation satisfying the law of trichotomy is sometimes said to be trichotomous.Trichotomous binary relations are equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath to tournamentsMathworldPlanetmath,although the study of tournaments is usually restricted to the finite case.

A transitiveMathworldPlanetmathPlanetmathPlanetmathPlanetmath trichotomous binary relation is called a total orderMathworldPlanetmath, and is typically written <.

The law of trichotomy for cardinal numbersMathworldPlanetmath is equivalent (in ZF) to the axiom of choiceMathworldPlanetmath (http://planetmath.org/AxiomOfChoice).

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更新时间:2025/5/4 16:21:30