This union of sets together is called the function's relative critical set.

Most simply, it may mean the union of sets that are disjoint.

Thus the two craft formed a precarious and narrow union of sets.

For a finite union of sets one often writes .

This principle gives us the cardinality of the union of sets.

Taking the intersection or the union of sets:

Addition of species is defined by the disjoint union of sets, and corresponds to a choice between structures.

I am trying to figure out what what would be the convex hull of an infinite union of sets.

Σ-types, also called dependent sum types, are analogous to the indexed disjoint unions of sets.

(One can show that R(S) is simply the set containing all finite unions of sets in S).

A set in a measure space is said to have σ-finite measure if it is a countable union of sets with finite measure.

For a given even ordinal α, B is the set of all wellordered unions of sets in B.

Addition of cardinal numbers is defined as the cardinality of the disjoint union of sets of given cardinalities.

The union of sets is distributive over intersection, and intersection is distributive over union.

Intersection and union of sets can be thought of in terms of the shaded regions in Fig. 0.1; such figures are called Venn diagrams.

For a semi-ring S, the set containing all finite disjoint unions of sets of S is the ring generated by S:

Analogous examples are given by the direct sum of vector spaces and modules, by the free product of groups and by the disjoint union of sets.

With sufficient imagination a man could write a whole series of versions of his life; it would form a union of sets in which the facts would be the only elements in common.

This means that there is a countable set S of open sets, such that every open set in X is the union of sets of the class S.

Further examples of commutative binary operations include addition and multiplication of complex numbers, addition and scalar multiplication of vectors, and intersection and union of sets.

The inclusion-exclusion principle, a formula for the size of a union of sets that may, together with another formula for the same union, be used as part of a double counting argument.

Probes with sequences which only occur once will identify clones lying in a contiguous region of the genome, while multiple-copy probes identify a union of sets of overlapping clones (Fig 1).

If we further assume that the relations are defined for all , then is an orthomodular lattice, while all the possible unions of sets of complete questions form a Boolean algebra with the as atoms.

In category theory, the coproduct, or categorical sum, is a category-theoretic construction which includes as examples the disjoint union of sets and of topological spaces, the free product of groups, and the direct sum of modules and vector spaces.

The conclusion of the theorem is a local statement, since a countable union of sets of measure zero is a set of measure zero, and the property of a subset of a coordinate patch having zero measure is invariant under diffeomorphism.