well-ordered set

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<mathematics> 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)

Nearby terms: well-behaved « well-connected « well-known port « well-ordered set » WEP » Wesley Clark » Western Digital Corporation

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