In fact, there are no two disjoint sets in this collection.

For more on disjointness in general, see: disjoint sets.

That is, if are pairwise disjoint sets, then we have:

The terminals and nonterminals of a particular grammar are two disjoint sets.

Curves whose interior zones do not intersect represent disjoint sets.

Near sets are disjoint sets that resemble each other.

In particular, the intersection of two disjoint sets is the empty set, which is convex.

This means that only collections of pairwise disjoint sets can be locally discrete.

The parameter space is partitioned into two disjoint sets and .

If and then there exists a finite number of mutually disjoint sets for such that .

Comparison of object descriptions provides a basis for determining the extent that disjoint sets resemble each other.

These groups of similar objects can provide information and reveal patterns about objects of interest in the disjoint sets.

With variables, a simple rule is required: parallel processes can only update disjoint sets of variables.

Alias classes are disjoint sets of locations that cannot alias to one another.

The separation axioms are about the use of topological means to distinguish disjoint sets and distinct points.

Songs that have more than one of these characteristics are quite rare, so his songs form three quite disjoint sets.

Let be a collection of disjoint sets, and let be integers with .

The disjoint union is also simple - for disjoint sets and , implies .

If one excludes currency from the definitions, the monetary base is not a subset of the money supply - rather, the two are disjoint sets.

More formally, the sum of the sizes of two disjoint sets is equal to the size of their union.

By deleting just one edge of the spanning tree, the vertices are partitioned into two disjoint sets.

Let , and be non-empty and disjoint sets.

Let be an m by n matrix whose rows can be partitioned into two disjoint sets and .

Every non-empty set x contains a member y such that x and y are disjoint sets.

The Jordan decomposition in measure theory says that every signed measure can be expressed as the difference of two positive measures supported on disjoint sets.