“intersection”的概念、定义、翻译、参考文献-科学参考

intersection

Mathematics

The intersection of sets A and B is the set consisting of all elements that belong to both A and B, and it is denoted by A ∩ B (read as ‘A intersect B’ or ‘A cap B’). The term ‘intersection’ is used for both the resulting set and the operation, a binary operation on the set of all subsets of a set. The following properties hold:
1. (i) For all A, A ∩ A = A and A∩Ø=Ø.
2. (ii) For all A and B, A ∩ B = B∩A; that is, ∩ is commutative.
3. (iii) For all A, B and C, (A ∩ B)∩ C = A∩(B ∩ C); that is, ∩ is associative.
Given a family of sets A_i with index set I, then the intersection

$⋂_{i \in I} A_{i}$

consists of those elements x such that x is an element of A_i for all i in I. For the intersection of two events, see event.

Statistics

The intersection of two events (see sample space) A and B is the event ‘both A and B occur’. It is denoted by A ∩ B. Clearly, for any events A, B, C, $intersection$ where S is the sample space and ϕ is the empty set. See also Boolean algebra; Venn diagram.
The intersection of the n events A₁, A₂,…, A_n is the event ‘all of A₁, A₂,…, A_n occur’. It is denoted by A₁ ∩ A₂ ∩…∩ A_n.
Intersection. This Venn diagram shows the intersection of two events as the overlapping part of the circles that represent the individual events.

Science and Technology

In mathematical set theory, the set between two sets A and B that contains only those elements of set A that also belong to set B (and vice versa), written as A∩B.
Mike Allaby

Computer

1. of sets. The set that results from combining elements common to two sets S and T, say, usually expressed as
$S \cap T$
∩ is regarded as an operation on sets, the intersection operation, which is commutative and associative. Symbolically
$\begin{array}{l} S \cap T = \\ {x | x \in S and x \in T} \end{array}$
When two sets S and T intersect in the empty set, the sets are disjoint. Since the intersection operation is associative, it can be extended to deal with the intersection of several sets.
2. of two graphs, G₁ and G₂. The graph that has as vertices those vertices common to G₁ and G₂ and as edges those edges common to G₁ and G₂.

Philosophy

An element belongs to the intersection of two sets, A and B if and only if it belongs to both A and B. The intersection is denoted by A ⋂ B.

单词	intersection
释义	intersection Mathematics The intersection of sets A and B is the set consisting of all elements that belong to both A and B, and it is denoted by A ∩ B (read as ‘A intersect B’ or ‘A cap B’). The term ‘intersection’ is used for both the resulting set and the operation, a binary operation on the set of all subsets of a set. The following properties hold: (i) For all A, A ∩ A = A and A∩Ø=Ø. (ii) For all A and B, A ∩ B = B∩A; that is, ∩ is commutative. (iii) For all A, B and C, (A ∩ B)∩ C = A∩(B ∩ C); that is, ∩ is associative. Given a family of sets A_i with index set I, then the intersection $⋂_{i \in I} A_{i}$ consists of those elements x such that x is an element of A_i for all i in I. For the intersection of two events, see event. Statistics The intersection of two events (see sample space) A and B is the event ‘both A and B occur’. It is denoted by A ∩ B. Clearly, for any events A, B, C, $intersection$ where S is the sample space and ϕ is the empty set. See also Boolean algebra; Venn diagram. The intersection of the n events A₁, A₂,…, A_n is the event ‘all of A₁, A₂,…, A_n occur’. It is denoted by A₁ ∩ A₂ ∩…∩ A_n. Intersection. This Venn diagram shows the intersection of two events as the overlapping part of the circles that represent the individual events. Science and Technology In mathematical set theory, the set between two sets A and B that contains only those elements of set A that also belong to set B (and vice versa), written as A∩B. Mike Allaby Computer 1. of sets. The set that results from combining elements common to two sets S and T, say, usually expressed as $S \cap T$ ∩ is regarded as an operation on sets, the intersection operation, which is commutative and associative. Symbolically $\begin{array}{l} S \cap T = \\ {x \| x \in S and x \in T} \end{array}$ When two sets S and T intersect in the empty set, the sets are disjoint. Since the intersection operation is associative, it can be extended to deal with the intersection of several sets. 2. of two graphs, G₁ and G₂. The graph that has as vertices those vertices common to G₁ and G₂ and as edges those edges common to G₁ and G₂. Philosophy An element belongs to the intersection of two sets, A and B if and only if it belongs to both A and B. The intersection is denoted by A ⋂ B.
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