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→通俗表达 Informal representation
In plain English, a hierarchy can be thought of as a set in which:
In plain English, a hierarchy can be thought of as a set in which:
在日常英语中，层次可以被看作是一个集合，其中:
# No element is superior to itself, and
# No element is superior to itself, and
No element is superior to itself, and
No element is superior to itself, and
任何元素都不高于自身，且
# One element, the ''hierarch'', is superior to all of the other elements in the set.
# One element, the ''hierarch'', is superior to all of the other elements in the set.
One element, the hierarch, is superior to all of the other elements in the set.
One element, the hierarch, is superior to all of the other elements in the set.
其中有一个层次元素，高于集合中的所有其他元素。
The first requirement is also interpreted to mean that a hierarchy can have no [[Cycle (graph theory)|circular relationships]]; the association between two objects is always [[Transitive relation|transitive]].
The first requirement is also interpreted to mean that a hierarchy can have no [[Cycle (graph theory)|circular relationships]]; the association between two objects is always [[Transitive relation|transitive]].
The first requirement is also interpreted to mean that a hierarchy can have no circular relationships; the association between two objects is always transitive.
The first requirement is also interpreted to mean that a hierarchy can have no circular relationships; the association between two objects is always transitive.
第一个前提也可理解为层次结构不能有循环关系; 两个对象之间的关联总是可传递的。
The second requirement asserts that a hierarchy must have a leader or [[root node|root]] that is common to all of the objects.
The second requirement asserts that a hierarchy must have a leader or [[root node|root]] that is common to all of the objects.
The second requirement asserts that a hierarchy must have a leader or root that is common to all of the objects.
The second requirement asserts that a hierarchy must have a leader or root that is common to all of the objects.
第二个要求则确定了层次结构必须有一个所有元素都共有的代表或根源。
==数学表达 Mathematical representation==
==数学表达 Mathematical representation==