Source : Free On-Line Dictionary of Computing

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)