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** A familiar real-life example of a partially ordered set is a collection of people ordered by genealogical descendancy. Some pairs of people bear the ancestor-descendant relationship, but other pairs bear no such relationship. | ** A familiar real-life example of a partially ordered set is a collection of people ordered by genealogical descendancy. Some pairs of people bear the ancestor-descendant relationship, but other pairs bear no such relationship. | ||
* (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Hierarchy_(mathematics) | * (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Hierarchy_(mathematics) | ||
** In mathematics, a hierarchy is a preorder, i.e. an ordered set. The term is used to stress a natural hierarchical relation among the elements. In particular, it is the preferred | ** In mathematics, a hierarchy is a preorder, i.e. an ordered set. The term is used to stress a natural hierarchical relation among the elements. In particular, it is the [[preferred term]]inology for posets whose elements are classes of objects of increasing complexity. In that case, the preorder defining the hierarchy is the class-containment relation. Containment hierarchies are thus special cases of hierarchies. | ||
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