Disjoint sets
Disjoint sets In mathematics, two sets are said to be disjoint if they have no element in common ... 2, 3} and {4, 5, 6} are disjoint sets. Explanation Formally, two sets A and B are disjoint if their intersection is the empty set ... of sets. A collection of sets is pairwise disjoint or mutually disjoint if any ...
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Disjoint union
Disjoint union Discriminated union links here. For discriminated ... see tagged union In set theory, a disjoint union (or discriminated union) is a union ... a collection of sets whose members are pairwise disjoint. Formally, if $C$ is a ... A \in C} A is a disjoint union if and only if for ...
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Almost disjoint sets
Almost disjoint sets In mathematics, two sets are almost disjoint if their intersection is small in some ... therefore result in different definitions of "almost disjoint". Definition The most common choice is to ... In this case, two sets are almost disjoint if their intersection is finite, i.e ... 0, 1] and [1, 2] are almost disjoint, because their intersection is the finite ...
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Glossary of graph theory
... a Hamiltonian path. Two paths are internally disjoint (some people call it independent) if they ... graph is the union of three internally disjoint (simple) paths that have the same two ... data structure). A forest is a vertex-disjoint union of trees; or, equivalently, an acyclic ... in a graph is a set of pairwise adjacent vertices. Since any subgraph induced by ... math>E_2 corresponds to a path(disjoint from all other such paths) in < ...
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Collision detection
... be possible to use a more specific pairwise pruning algorithm as discussed below, and an ... and the size of the time step. Pairwise pruning Once we've selected a pair ... as splines instead of simple triangles. Exact pairwise collision detection Once we're done pruning ... for any two convex objects which are disjoint, one can find a plane in space ... then the triangles are deemed to be disjoint. On the other hand, if none ...
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Set packing
... some k subsets in the list are pairwise disjoint (in other words, no two of them ... we can easily verify that they are pairwise disjoint. The NP-hard optimization version of the ... packing, asks for the maximum number of pairwise disjoint sets in the list. Example ...
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Quantum logic
... perp . Q is also sequentially complete: any pairwise disjoint sequence{V i } i of elements of ... for any sequence {S i } i of pairwise disjoint Borel subsets of R, {φ(S i )} i are pairwise orthogonal projections and $\backslash phi(\backslash bigcup\_\{\; ...$
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Carathéodory's extension theorem
... cap B \in S (closed under pairwise intersections) For all $A,\; B\; \backslash in\; S$, there exist disjoint sets $K\_i\; \backslash in\; S$, with ... relative complements can be written as finite disjoint unions). With the same notation, we define ... cup B \in R (closed under pairwise unions) For all $A,\; B\; \backslash in\; ...\; the\; measure\; theory\; context:\; \Omega \; is\; the$disjoint union of a countable family of ...
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Tsirelson's bound
... distinct from each other (though not necessarily disjoint); set J contained trials which were not ... experimental data collected in four (not necessarily disjoint) sets of trials J, K, L, and ... above as obtained in four (not necessarily disjoint) sets of trials J, K, L, and ... A↑) (B «) ( M ) are not all pairwise equal, or correspondingly, even if the four ... and φ M , did not all have pairwise equal value. Under these stronger assumptions, ...
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Talk:Curve/archive1
... which are not, based on comparing the pairwise distances). Finally, if you insist on particular ... intersect I, thus O and I are disjoint; therefore, the real number line R is ... containing 3 points of B and is disjoint from I, so the real line is ... the same four boundary points, but nevertheless disjoint interiors. Accounting for all this, I'd ... then T is the union of two disjoint non-empty closed subsets of X. - - ...
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