[1] : The Free On-line Dictionary of Computing (27 SEP 03)

well-ordered set
     
         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.
     
        1995-04-19
     
     
see also:
total ordering chains ordinals isomorphism classes well-ordered sets integers 

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