This article is about the mathematical concept. For the data structure, see Disjoint-set data structure.
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 or more sets is called disjoint if any two distinct sets of the collection are disjoint.
^Halmos, P. R. (1960), Naive Set Theory, Undergraduate Texts in Mathematics, Springer, p. 15, ISBN 9780387900926.
are sets whose intersection is the empty set. For example, {1, 2, 3} and {4, 5, 6} are disjointsets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A...
In mathematics, the disjoint union (or discriminated union) A ⊔ B {\displaystyle A\sqcup B} of the sets A and B is the set formed from the elements of...
disjoint, because their intersection is infinite. This definition extends to any collection of sets. A collection of sets is pairwise almost disjoint...
Look up disjoint in Wiktionary, the free dictionary. Disjoint may refer to: Disjointsets, sets with no common elements Mutual exclusivity, the impossibility...
a maximum disjointset (MDS) is a largest set of non-overlapping geometric shapes selected from a given set of candidate shapes. Every set of non-overlapping...
{C}}\subseteq {\mathcal {S}}} of sets such that all sets in C {\displaystyle {\mathcal {C}}} are pairwise disjoint. The size of the packing is | C |...
these subsets (i.e., the subsets are nonempty mutually disjointsets). Equivalently, a family of sets P is a partition of X if and only if all of the following...
Fuzzy sets are disjoint if and only if their supports are disjoint according to the standard definition for crisp sets. For disjoint fuzzy sets A , B...
two disjointsets of natural numbers are called computably inseparable or recursively inseparable if they cannot be "separated" with a computable set. These...
{\displaystyle n=2^{(k+1)}-2} elements. The set system consists of k {\displaystyle k} pairwise disjointsets S 1 , … , S k {\displaystyle S_{1},\ldots...
different notions of a ring of sets, both referring to certain families of sets. In order theory, a nonempty family of sets R {\displaystyle {\mathcal {R}}}...
\mathbb {R} /\mathbb {Q} } partition R {\displaystyle \mathbb {R} } into disjointsets, and each element is dense in R {\displaystyle \mathbb {R} } . Each...
numbers and the interval [ 0 , 1 ] {\displaystyle [0,1]} . If A and B are disjointsets, then | A ∪ B | = | A | + | B | . {\displaystyle \left\vert A\cup B\right\vert...
of the set, and the exterior, which represents all elements that are not members of the set. Curves which do not overlap represent disjointsets, which...
the disjoint union of graphs is an operation that combines two or more graphs to form a larger graph. It is analogous to the disjoint union of sets, and...
symmetric difference of two sets, also known as the disjunctive union and set sum, is the set of elements which are in either of the sets, but not in their intersection...
that, for disjointsets A and B, we have | A ∪ B | = | A | + | B | {\displaystyle |A\cup B|=|A|+|B|} , provided that the intersection of the sets is without...
separation axioms are about the use of topological means to distinguish disjointsets and distinct points. It's not enough for elements of a topological space...
mathematics, a superadditive set function is a set function whose value when applied to the union of two disjointsets is greater than or equal to the...
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