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    Well Ordered Set

    Definition

    A totally ordered set (A, <=) is said to be well ordered (or have a well-founded order) iff every nonempty subset of A has a least element. Every finite totally ordered set is well ordered. The set of integers Z, which has no least element, is an example of a set that is not well ordered. An ordinal number is the order type of a well ordered set.

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