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well-ordered set
<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)
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Nearby terms:
well-behaved « well-connected « well-known port « well-ordered set » Wesley Clark » Western Digital Corporation » Westmount
This article was derived from the Free Online Dictionary of Computers and is available under ther terms of the GNU Free Documentation License.
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