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Meaning of WELL-ORDERED SET

 
Computing Dictionary
 
 Definition: 

A set with a total ordering and no infinite descending chains. A total ordering "<=" satisfies

        x <= x
        x <= y <= z  =>  x <= z
        x <= y <= x  =>  x = y
        for all x, y: x <= y or y <= x

In addition, if a set W is well-ordered then all non-empty subsets A of W have a least element, i.e. there exists x in A such that for all y in A, x <= y.

ordinals are isomorphism classes of well-ordered sets, just as integers are isomorphism classes of finite sets.

 

 

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