Nested set collection

It is used as reference concept in scientific hierarchy definitions, and many technical approaches, like the tree in computational data structures or nested set model of relational databases.

[2] In particular, when scanning all pairs of subsets at the second condition, it is true for any combination with B.

Using a set of atomic elements, as the set of the playing card suits: The second condition of the formal definition can be checked by combining all pairs: There is a hierarchy that can be expressed by two branches and its nested order: B3 ⊂ B2 ⊂ B;  B1 ⊂ B.

[3] The concept of nesting is exemplified in Russian matryoshka dolls.

Illustrating the general concept: A square can always also be referred to as a quadrilateral, polygon or shape.

Nested hierarchies are the organizational schemes behind taxonomies and systematic classifications.

A nested set of Russian dolls .
Nested set representing a biological taxonomy example. Outside-in: order, family, genus, species.
Expressing the example as a partially ordered set by its Hasse diagram .