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well-ordered set


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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.


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