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第295行：
第295行： − + − [俄罗斯套娃，又称嵌套娃娃或俄罗斯套娃。每个洋娃娃都被包裹在另一个洋娃娃里面，直到最小的洋娃娃被够到。这就是嵌套的概念。当这个概念应用于集合时，结果排序是一个嵌套的层次结构。]] 第303行：
第302行： − 嵌套层次结构或包含层次结构是嵌套集的层次结构排序。嵌套的概念在俄罗斯套娃中得到了体现。每个娃娃都被另一个娃娃包围着，一直到外面的娃娃。外部的玩偶包含所有的内部玩偶，下一个外部的玩偶包含所有剩余的内部玩偶，等等。表示一个嵌套层次结构，其中每个层次只包含一个对象，也就是说，每个娃娃的大小只有一个; 一个广义的嵌套层次结构允许在层次中有多个对象，但每个对象在每个层次上只有一个父对象。一般概念在下面的例子中得到了证明和数学上的表述:+ − − 嵌套层次结构或包含层次结构是嵌套集的层次结构排序。嵌套的概念在俄罗斯套娃中得到了体现。每个娃娃都被另一个娃娃包围着，一直到外面的娃娃。外部的玩偶包含所有的内部玩偶，下一个外部的玩偶包含所有剩余的内部玩偶，等等。表示一个嵌套层次结构，其中每个层次只包含一个对象，也就是说，每个娃娃的大小只有一个; 一个广义的嵌套层次结构允许在层次中有多个对象，但每个对象在每个层次上只有一个父对象。一般概念在下面的例子中得到了证明和数学上的表述: 第321行：
第318行： − 正方形也可以称为四边形、多边形或形状。这样看来，它是一个等级制度。但是，请考虑使用这种分类的多边形集。正方形只能是四边形，不能是三角形、六边形等等。+ + 第329行：
第327行： − 嵌套的层次结构是分类法和系统分类法背后的组织方案。例如，使用最初的林奈分类法(他在《自然系统》第10版中列出的版本) ，人类可以被规划为:+ 第345行：
第343行： − 分类法可能会频繁更改(如在生物分类法中所见) ，但是嵌套层次结构的基本概念始终是相同的。+ + 第353行：
第352行： − 在许多编程分类法和语法模型(以及数学中的分形)中，嵌套的层次结构，包括俄罗斯娃娃，也被用来说明自相似和递归的性质。递归本身是层次编程的一个子集，递归思维可以是层次思维和逻辑的同义词。+ − −
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[[Matryoshka dolls, also known as nesting dolls or Russian dolls. Each doll is encompassed inside another until the smallest one is reached. This is the concept of nesting. When the concept is applied to sets, the resulting ordering is a nested hierarchy.]]
[[Matryoshka dolls, also known as nesting dolls or Russian dolls. Each doll is encompassed inside another until the smallest one is reached. This is the concept of nesting. When the concept is applied to sets, the resulting ordering is a nested hierarchy.]]
[俄罗斯套娃，又称嵌套娃娃或俄罗斯套娃。每个洋娃娃都被包裹在另一个洋娃娃里面，直到最小的洋娃娃被够到。这就是嵌套的概念。当这个概念应用于集合时，结果排序是一个嵌套的层次结构。]]
[玛特罗什卡套娃，又称嵌套娃娃或俄罗斯套娃。每个洋娃娃都被包裹在另一个洋娃娃里面，直到最小的洋娃娃。这就是嵌套的概念。当这个概念应用于集合时，其结果排序是一个嵌套的层次结构。]]
A nested hierarchy or ''inclusion hierarchy'' is a hierarchical ordering of [[nested set]]s.<ref name="natsocsci-ch4">{{cite encyclopedia|title=Hierarchy, Complexity, Society|last=Lane|first=David|pages=81–120|encyclopedia=Hierarchy in Natural and Social Sciences|editor=Pumain, Denise|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}</ref> The concept of nesting is exemplified in Russian [[matryoshka doll]]s. Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll; a generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example:
A nested hierarchy or ''inclusion hierarchy'' is a hierarchical ordering of [[nested set]]s.<ref name="natsocsci-ch4">{{cite encyclopedia|title=Hierarchy, Complexity, Society|last=Lane|first=David|pages=81–120|encyclopedia=Hierarchy in Natural and Social Sciences|editor=Pumain, Denise|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}</ref> The concept of nesting is exemplified in Russian [[matryoshka doll]]s. Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll; a generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example:
A nested hierarchy or inclusion hierarchy is a hierarchical ordering of nested sets. The concept of nesting is exemplified in Russian matryoshka dolls. Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll; a generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example:
A nested hierarchy or inclusion hierarchy is a hierarchical ordering of nested sets. The concept of nesting is exemplified in Russian matryoshka dolls. Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll; a generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example:
嵌套层次结构或包含层次结构是嵌套集的层次结构排序。嵌套的概念在俄罗斯套娃中得到了体现。每个洋娃娃都被另一个洋娃娃包裹着，一直到最外层的。外部的洋娃娃包含所有其内部的洋娃娃，往外一层的洋娃娃也包含所有其内部剩余的洋娃娃，如此反复。套娃结构是一个每层都只有一个对象的嵌套层次结构，例如在套娃中同样大小的洋娃娃只有一个；广义的嵌套层次可以每层都有多个对象，但每层里的对象都只有一个父级对象。嵌套层次的一般概念的论证及数学表达如下：
A square can always also be referred to as a quadrilateral, polygon or shape. In this way, it is a hierarchy. However, consider the set of polygons using this classification. A square can only be a quadrilateral; it can never be a triangle, hexagon, etc.
A square can always also be referred to as a quadrilateral, polygon or shape. In this way, it is a hierarchy. However, consider the set of polygons using this classification. A square can only be a quadrilateral; it can never be a triangle, hexagon, etc.
正方形可称为四边形、多边形或形状。这样看来是层次性的。然而若多边形集采用这种分类法，则正方形只能是四边形，而不会是三角形、六边形等。
Nested hierarchies are the organizational schemes behind taxonomies and systematic classifications. For example, using the original Linnaean taxonomy (the version he laid out in the 10th edition of Systema Naturae), a human can be formulated as:
Nested hierarchies are the organizational schemes behind taxonomies and systematic classifications. For example, using the original Linnaean taxonomy (the version he laid out in the 10th edition of Systema Naturae), a human can be formulated as:
嵌套层次结构是分类学和系统分类背后的组织性方案。例如，在最初的林奈分类法（他在《自然系统》第10版中所列）中，人类可被归为
Taxonomies may change frequently (as seen in biological taxonomy), but the underlying concept of nested hierarchies is always the same.
Taxonomies may change frequently (as seen in biological taxonomy), but the underlying concept of nested hierarchies is always the same.
分类法可能会频繁改变（如在生物分类法中所见），但嵌套层次结构这一基本概念始终不变。
In many programming taxonomies and syntax models (as well as fractals in mathematics), nested hierarchies, including Russian dolls, are also used to illustrate the properties of self-similarity and recursion. Recursion itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic.
In many programming taxonomies and syntax models (as well as fractals in mathematics), nested hierarchies, including Russian dolls, are also used to illustrate the properties of self-similarity and recursion. Recursion itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic.
在许多编程分类法和句法模型(以及数学中的分形)中，包括俄罗斯娃娃，嵌套的层次结构也用作自相似和递归性质的呈现。递归本身是层次性编程的一个子集，递归思维可用作层次思维和逻辑的同义词。
===包容层次 Containment hierarchy===
===包容层次 Containment hierarchy===