Overview

# well-ordered set

#### More Like This

Show all results sharing this subject:

• Computing

GO

Show Summary Details

## Quick Reference

A set S on which the relation < is defined, satisfying the following properties:(a) given x,y,z in S, if x < y and y < z, then x < z(b) given x,y in S, then exactly one of the following three possibilities is true: x < y, x = y, or y < x(c) if T is any nonempty subset of S, then there exists an element x in T such that x = y or x < y, i.e. xy for all y in T This relation < is said to be a well ordering of the set S.

(a) given x,y,z in S, if x < y and y < z, then x < z

(b) given x,y in S, then exactly one of the following three possibilities is true: x < y, x = y, or y < x

x < y, x = y, or y < x

(c) if T is any nonempty subset of S, then there exists an element x in T such that x = y or x < y, i.e. xy for all y in T

x = y or x < y,

Subjects: Computing.

##### Reference entries

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.