Containment hierarchy
 | This article may be confusing or unclear to readers. In particular, is this supposed to be a mathematical hierarchy (hierarchy (mathematics)) or a hierarchical structure?? It is defined as the first, and is referred to in the corresponding article, yet all the examples are structural hierarchies. Yes, they're related, but be consistent!. (October 2009) |
 | This article needs attention from an expert on the subject. The specific problem is: see notes above.. (October 2009) |
A containment hierarchy is a hierarchical collection of strictly nested sets. Each entry in the hierarchy designates a set of which the previous entry is a strict superset, and the next entry is a strict subset. For example, all rectangles are quadrilaterals, but not all quadrilaterals are rectangles, and all squares are rectangles, but not all rectangles are squares. A hierarchy of this kind is to be contrasted with a more general notion of a partially ordered set.
A taxonomy is a classic example of a containment hierarchy.
Examples
- Geometry
- shape → polygon → quadrilateral → rectangle → square
- Particle physics
- particle → elementary particle → fermion → lepton → electron
- Philosophy
- abstract → concept → idea → application → concrete
- Biology
- Biological classification: animal → bird → raptor → eagle → golden eagle
- Hierarchy of life: organism → organ system → organ → tissue → cell
- Formal grammars
- Chomsky hierarchy: unrestricted → context-sensitive → context-free → regular
See also
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