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单词 WellOrderedSet
释义

well ordered set


A well-ordered set is a totally ordered setMathworldPlanetmath in which every nonempty subset has a least member.

An example of well-ordered set is the set of positive integers with the standard order relation (+,<), because any nonempty subset of it has least member. However, + (the positive reals) is not a well-ordered set with the usual order, because (0,1)={x:0<x<1} is a nonempty subset but it doesn’t contain a least number.

A well-ordering of a set X is the result of defining a binary relationMathworldPlanetmath on X to itself in such a way that X becomes well-ordered with respect to .

Titlewell ordered set
Canonical nameWellOrderedSet
Date of creation2013-03-22 11:47:22
Last modified on2013-03-22 11:47:22
Ownerdrini (3)
Last modified bydrini (3)
Numerical id16
Authordrini (3)
Entry typeDefinition
Classificationmsc 03E25
Classificationmsc 06A05
Classificationmsc 81T17
Classificationmsc 81T13
Classificationmsc 81T75
Classificationmsc 81T45
Classificationmsc 81T10
Classificationmsc 81T05
Classificationmsc 42-02
Classificationmsc 55R15
Classificationmsc 47D03
Classificationmsc 55U35
Classificationmsc 55U40
Classificationmsc 47D08
Classificationmsc 55-02
Classificationmsc 18-00
Synonymwell-ordered
Synonymwell-ordered set
Related topicWellOrderingPrinciple
Related topicNaturalNumbersAreWellOrdered
Defineswell-ordering
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更新时间:2025/5/4 5:06:53