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A containment hierarchy is a direct extrapolation of the nested hierarchy concept. All of the ordered sets are still nested, but every set must be "strict"—no two sets can be identical. The shapes example above can be modified to demonstrate this:

A containment hierarchy is a direct extrapolation of the nested hierarchy concept. All of the ordered sets are still nested, but every set must be "strict"—no two sets can be identical. The shapes example above can be modified to demonstrate this:

包容层次结构是嵌套层次结构概念的直接外推。所有的有序集仍然是嵌套的，但是每个集合必须是“严格”的ーー没有两个集合是相同的。上面的图形例子可以通过修改来演示:

包容层次是嵌套层次概念的直接外推。所有的有序集仍然是嵌套的，但是每个集合必须是“严格”的——不存在两个相同的集合。上面的图形示例可稍作改变来论证:

The notation <math> x \subsetneq y \, </math> means x is a subset of y but is not equal to&nbsp;y.

The notation <math> x \subsetneq y \, </math> means x is a subset of y but is not equal to&nbsp;y.

符号 < math > x subsetneq y，</math > 表示 x 是 y 的子集，但不等于 y。

符号 < math > x subsetneq y，</math > 表示x是y的子集，但不等于y。

A general example of a containment hierarchy is demonstrated in class inheritance in object-oriented programming.

A general example of a containment hierarchy is demonstrated in class inheritance in object-oriented programming.

 

Two types of containment hierarchies are the subsumptive containment hierarchy and the compositional containment hierarchy. A subsumptive hierarchy "subsumes" its children, and a compositional hierarchy is "composed" of its children. A hierarchy can also be both subsumptive and compositional.

Two types of containment hierarchies are the subsumptive containment hierarchy and the compositional containment hierarchy. A subsumptive hierarchy "subsumes" its children, and a compositional hierarchy is "composed" of its children. A hierarchy can also be both subsumptive and compositional.