Search results
Results from the WOW.Com Content Network
In category theory the disjoint union is defined as a coproduct in the category of sets. As such, the disjoint union is defined up to an isomorphism, and the above definition is just one realization of the coproduct, among others. When the sets are pairwise disjoint, the usual union is another realization of the coproduct.
Two disjoint sets. In set theory in mathematics and formal logic, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set. [1] For example, {1, 2, 3} and {4, 5, 6} are disjoint sets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A collection of two ...
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
Applied to Sets. In the terms of a set: "If the finite set A is the union of n pairwise disjoint subsets each with d elements, then n = |A|/d." [1] As a function
If A is a union of countably many pairwise disjoint Lebesgue-measurable sets, then A is itself Lebesgue-measurable and λ(A) is equal to the sum (or infinite series) of the measures of the involved measurable sets. If A is Lebesgue-measurable, then so is its complement. λ(A) ≥ 0 for every Lebesgue-measurable set A.
The set of those translates partitions the circle into a countable collection of pairwise disjoint sets, which are all pairwise congruent. Since X is not measurable for any rotation-invariant countably additive finite measure on S , finding an algorithm to form a set from selecting a point in each orbit requires that one add the axiom of choice ...
Moreover, the elements of P are pairwise disjoint and their union is ... Just as order relations are grounded in ordered sets, sets closed under pairwise supremum and ...
Each ellipse is a connected set, but the union is not connected, since it can be partitioned to two disjoint open sets and . This means that, if the union X {\displaystyle X} is disconnected, then the collection { X i } {\displaystyle \{X_{i}\}} can be partitioned to two sub-collections, such that the unions of the sub-collections are disjoint ...