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Intersection set theory - Nullary intersection

A Wisdom Archive on Intersection set theory - Nullary intersection

Intersection set theory - Nullary intersection

A selection of articles related to Intersection set theory - Nullary intersection

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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

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Intersection set theory - Nullary intersection: Encyclopedia II - Intersection set theory - Nullary intersection

Note that in the previous section we excluded the case where M was the empty set (∅). The reason is the follows. The intersection of the collection M is defined as the set (see set-builder notation) If M is empty there are no sets A in M, so the question becomes "which x's satisfy the stated condition?" The answer seems to be every possible x. When M is empty the condition given above is an example of a vacuous truth. So the intersection of the empty family ...

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Intersection set theory, Intersection set theory - Basic definition, Intersection set theory - Arbitrary intersections, Intersection set theory - Nullary intersection

Read more here: » Intersection set theory: Encyclopedia II - Intersection set theory - Nullary intersection

Intersection set theory - Nullary intersection: Encyclopedia II - Intersection set theory - Arbitrary intersections

The most general notion is the intersection of an arbitrary nonempty collection of sets. If M is a nonempty set whose elements are themselves sets, then x is an element of the intersection of M if and only if for every element A of M, x is an element of A. In symbols: This idea subsumes the above paragraphs, in that for example, A ∩B ∩C ...

See also:

Intersection set theory, Intersection set theory - Basic definition, Intersection set theory - Arbitrary intersections, Intersection set theory - Nullary intersection

Read more here: » Intersection set theory: Encyclopedia II - Intersection set theory - Arbitrary intersections

Intersection set theory - Nullary intersection: 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

Read more here: » Intersection set theory: Encyclopedia II - Intersection set theory - Basic definition

More material related to Intersection Set Theory can be found here:
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Intersection Set Theory
Index of Articles
related to
Intersection Set Theory
Index of Articles
related to
Intersection set theory -...



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