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Cartesian product of sets A and B is finite then does it follow that A and B are finite?
Wiki User
∙ 14y ago
The number of elements in a Cartesian product is equal to the product in the number of elements of each set. The idea of a Cartesian product is that you combine each element from set A with each element from set B. If the product set (the Cartesian product) of sets A and B has a finite number of elements, this may be due to the fact that both A and B are finite. However, there is another possibility: that one of the sets, for example, set A, has zero elements, and the other is infinite. In this case, the Cartesian product would also have zero elements.
Wiki User
∙ 14y ago
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Prove that a finite cartesian product of countable sets is countable?
here is the proof: http://planetmath.org/encyclopedia/ProductOfAFiniteNumberOfCountableSetsIsCountable.html
What is the Cartesian product of two sets?
If S and T are any two sets, then their Cartesian product, written S X T, is the set of all of the ordered pairs {s, t} such that s Є Sand t Є T.For some basic set theory, follow the related link.Also, the Cartesian product is used in the definition of "relation" and "metric." Follow the corresponding links for more information.
What is the Cartesian product?
A Cartesian product of two sets is a set that contains all ordered pairs, such that the first item is from the first set and the second item from the second set. (It can be the same set twice, instead of two different sets.) For example, the Cartesian product of the sets {A, B} and {1, 2, 3} is the set of pairs: {(A, 1), (A, 2), (A, 3), (B, 1), (B, 2), (B, 3)} In general, the Cartesian product has a number of elements that is the product of the number of elements of the two products that make it up. A Cartesian product can also be defined for more than two sets. Cartesian products are very important as the basis of mathematics. For example, relations are subsets of Cartesian products. Note that functions are a special type of relation.
What is the magnitude of cartesian product?
The Cartesian product of two sets, A and B, where A has m distinct elements and B has n, is the set of m*n ordered pairs. The magnitude is, therefore m*n.
Is the union of finite countable sets finite?
YES
Prove that a finite cartesian product of countable sets is countable?
here is the proof: http://planetmath.org/encyclopedia/ProductOfAFiniteNumberOfCountableSetsIsCountable.html
What is the Cartesian product of two sets?
If S and T are any two sets, then their Cartesian product, written S X T, is the set of all of the ordered pairs {s, t} such that s Є Sand t Є T.For some basic set theory, follow the related link.Also, the Cartesian product is used in the definition of "relation" and "metric." Follow the corresponding links for more information.
A set of ordered pairs is called?
Cartesian product is the name that refers to the set of the ordered pairs. The Cartesian product of two sets A and B is AB.
What is the Cartesian product?
A Cartesian product of two sets is a set that contains all ordered pairs, such that the first item is from the first set and the second item from the second set. (It can be the same set twice, instead of two different sets.) For example, the Cartesian product of the sets {A, B} and {1, 2, 3} is the set of pairs: {(A, 1), (A, 2), (A, 3), (B, 1), (B, 2), (B, 3)} In general, the Cartesian product has a number of elements that is the product of the number of elements of the two products that make it up. A Cartesian product can also be defined for more than two sets. Cartesian products are very important as the basis of mathematics. For example, relations are subsets of Cartesian products. Note that functions are a special type of relation.
What is the magnitude of cartesian product?
The Cartesian product of two sets, A and B, where A has m distinct elements and B has n, is the set of m*n ordered pairs. The magnitude is, therefore m*n.
What are finite sets?
They are sets with a finite number of elements. For example the days of the week, or the 12 months of the year. Modular arithmetic is based on finite sets.
What is the kinds of sets?
Closed sets and open sets, or finite and infinite sets.
Is the union of finite countable sets finite?
YES
Give you examples of finite sets of numbers?
sets
What is the two kind of sets?
Closed sets and open sets, or finite and infinite sets.
How is a relation between two sets defined?
A relation between two sets is defined to be any subset of the two set's Cartesian product. See related links for more information and an example.
What is kind of set?
Closed sets and open sets, or finite and infinite sets.
