A formal sum of elements of a given set B is an element of the free abelian group with basis B.

In other words, given a set B, let G be the unique (up to isomorphism) free abelian group with basis B.

The second term converges to zero as δ 0, since the set B shrinks to an empty set.

The relative complement of A in B is the set B without all the elements of A:

Due to differing vehicle construction, car 1004 in set B had unusual elongated hexagonal windows.

Vector spaces: The set A is an Abelian group, and the set B is a field.

Group with operators: In this case, the set A is a group, and the set B is just a set.

There exists a set B whose members are precisely those objects that satisfy the predicate φ.

Similarly, an index for a set B describes the computable function enumerating the basic open sets in the complement of B.

A set B is if and only if .