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In computer science, a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of disjoint (non-overlapping) sets. Equivalently, it stores a partition of a set into disjoint subsets .
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 ...
In the examples below, the Euler diagram depicts that the sets Animal and Mineral are disjoint since the corresponding curves are disjoint, and also that the set Four Legs is a subset of the set of Animals. The Venn diagram, which uses the same categories of Animal, Mineral, and Four Legs, does not encapsulate these relationships.
In mathematics, the disjoint union (or discriminated union) of the sets A and B is the set formed from the elements of A and B labelled (indexed) with the name of the set from which they come. So, an element belonging to both A and B appears twice in the disjoint union, with two different labels.
Intersecting and disjoint sets [ edit ] We say that A {\displaystyle A} intersects (meets) B {\displaystyle B} if there exists some x {\displaystyle x} that is an element of both A {\displaystyle A} and B , {\displaystyle B,} in which case we also say that A {\displaystyle A} intersects (meets) B {\displaystyle B} at x {\displaystyle x} .
A partition of a set X is a set of non-empty subsets of X such that every element x in X is in exactly one of these subsets [2] (i.e., the subsets are nonempty mutually disjoint sets). Equivalently, a family of sets P is a partition of X if and only if all of the following conditions hold: [3]
Equivalently, two sets are linearly separable precisely when their respective convex hulls are disjoint (colloquially, do not overlap). [ 1 ] In simple 2D, it can also be imagined that the set of points under a linear transformation collapses into a line, on which there exists a value, k, greater than which one set of points will fall into, and ...
A most basic way in which two sets can be separated is if they are disjoint, that is, if their intersection is the empty set. This property has nothing to do with topology as such, but only set theory. Each of the following properties is stricter than disjointness, incorporating some topological information.