Containment hierarchy: Difference between revisions

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#REDIRECT [[Hierarchy#Containment hierarchy]]

{{confusing|date=October 2009|reason=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!}}

{{expert|date=October 2009|reason=see notes above.}}

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A '''containment hierarchy''' is a [[hierarchical]] collection of strictly nested [[Set (mathematics)|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]].

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A [[taxonomy]] is a classic example of a containment hierarchy.

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==Examples==

;[[Geometry]]:[[shape]] → [[polygon]] → [[quadrilateral]] → [[rectangle]] → [[Square (geometry)|square]]

;[[Particle physics]]:[[subatomic particle|particle]] → [[elementary particle]] → [[fermion]] → [[lepton]] → [[electron]]

;[[Philosophy]]: [[Abstract object|abstract]] → [[concept]] → [[idea]] → application → [[concrete object|concrete]]

;[[Biology]]: [[Biological classification]]: [[animal]] → [[bird]] → [[bird of prey|raptor]] → [[eagle]] → [[golden eagle]]

: [[Hierarchy of life]]: [[organism]] → [[organ system]] → [[organ (anatomy)|organ]] → [[tissue (biology)|tissue]] → [[cell (biology)|cell]]

;[[Formal grammar]]s:[[Chomsky hierarchy]]: [[unrestricted grammar|unrestricted]] → [[context-sensitive grammar|context-sensitive]] → [[context-free grammar|context-free]] → [[regular grammar|regular]]

== See also ==

* [[Cladistics]]

* [[Hierarchy (mathematics)]]

[[Category:Hierarchy]]

[[Category:Classification algorithms]]

[[Category:Set families]]

[[Category:Taxonomy]]

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