Containment hierarchy

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

See also

• Cladistics
• Hierarchy (mathematics)