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A 'containment hierarchy' is a hierarchical collection of strictly nested sets. Each entry in the hierarchy designates a set such that 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:

★ In geometry: shape -> polygon -> quadrilateral -> rectangle -> square

★ In biology: animal -> bird -> raptor -> eagle -> golden eagle

★ The Chomsky hierarchy in formal languages: recursively enumerable -> context-sensitive -> context-free -> regular

★ In physics: particle -> elementary particle -> fermion -> lepton -> electron

★ In philosophy: abstract -> concept -> idea -> application -> concrete

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See also

See also

★ Cladistics

★ Hierarchy (mathematics)