We have two kinds of description (words) for denoting a data-cluster: a "class" and a "set."

　A "class" is a "category" to group any set of persons or things together: let a class of "customer" be expressed as a data-cluster (stored) in a clothing (apparel) store, and the store has trinomial data of customers such as "man", "woman" and "corporate body"--they are the pairwise disjoint union of "customer"--, then an "individual" customer is a "class" to put together the set of "man" and the set of "woman", and likewise a "customer" is a higher class for both an "individual" and "institutional" customers.

　A decomposition of "customer" into classes--"man", "woman" and "corporate body"--is called "partition" of "customer."

Note:

1. Trinomial (three kinds of) data in sets:

(1) "man"　｛Masami S., Wittgenstein L.,...｝
(2) "woman"　｛Emiko S., Mitsuko T.,...｝
(3) "corporation"　｛HONDA, TOYOTA,...｝

2. Then we have a hierarchical data structure as noted below:

　customer
　　｜
　　｜＿＿＿＿ individual customer
　　｜
　　｜＿＿＿＿ instutional customer

　individual customer
　　｜
　　｜＿＿＿＿ man
　　｜
　　｜＿＿＿＿ woman

　A set is mathematically a data-cluster of objects, and the objects in a set are called its "members" or "elements." If "a" is an element of the set A, we say "'a' belongs to A" and denote it as noted below:
　　　　　　　　　a ∈ A.

　A set is, from the view point of "entity-relationship" model, equivalent to an entity.

　If every element of a set A is an element of a set B, that is if a ∈ A then a ∈ B, A is called a "subset" of B. A is contained in B, or B contains A, we write A ⊂ B or B ⊃ A.
　It can be consequently said that the data-clusters of "man" and "woman," in the example mentioned above, are the subsets of "individual," and that the "individual" and "institutional" are the subsets of the "customer."

　As we can see, a "class" and a "set" is the two sides of the same coin--to be exact, they make a difference in the mathematical definition, but I should not worry about it here because it may be noninformation for the topic that we are talking about today.