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Intersection set theory - Basic definition | | Intersection set theory - Basic definition: Encyclopedia II - Intersection set theory - Basic definition | | The intersection of A and B is written "A ∩ B". Formally:
x is an element of A ∩ B if and only if
x is an element of A and
x is an element of B.
For example, the intersection of the sets {1, 2, 3} and {2, 3, 4} is {2, 3}. The number 9 is not contained in the intersection of the set of prime numbers
{2, 3, 5, 7, 11, … ...
See also:Intersection set theory, Intersection set theory - Basic definition, Intersection set theory - Arbitrary intersections, Intersection set theory - Nullary intersection | | | Intersection set theory, Intersection set theory - Arbitrary intersections, Intersection set theory - Basic definition, Intersection set theory - Nullary intersection, Naive set theory, Union, Complement, Symmetric difference | | |
| | | Intersection set theory: Encyclopedia II - Intersection set theory - Basic definition
Intersection set theory - Basic definition
The intersection of A and B is written "A ∩ B". Formally:
x is an element of A ∩ B if and only if
- x is an element of A and
- x is an element of B.
For example, the intersection of the sets {1, 2, 3} and {2, 3, 4} is {2, 3}. The number 9 is not contained in the intersection of the set of prime numbers
{2, 3, 5, 7, 11, …} and the set of odd numbers
{1, 3, 5, 7, 9, 11, …}.
If the intersection of two sets A and B is empty, that is they have no elements in common, then they are said to be disjoint, denoted: A ∩ B = Ø. For example the sets {1, 2} and {3, 4} are disjoint, written
{1, 2} ∩ {3, 4} = Ø.
More generally, one can take the intersection of several sets at once. The intersection of A, B, C, and D, for example, is A ∩ B ∩ C ∩ D = A ∩ (B ∩ (C ∩ D)). Intersection is an associative operation; thus,
A ∩ (B ∩ C) = (A ∩ B) ∩ C.
Other related archivesAbstract algebra, Algebra, Cantor's paradox, Complement, HTML, Naive set theory, Set theory, Symmetric difference, Union, and, associative, character entity, empty set, for every, if and only if, index set, infinite series, mathematics, naive set theory, natural numbers, nonempty, prime numbers, set theorists, set-builder notation, sets, table of mathematical symbols, universe, vacuous truth, σ-algebras
 Adapted from the Wikipedia article "Basic definition", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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