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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.
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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.
Cartesian product of sets A and B is finite then does it follow that A and B are finite?
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.
Prove that a finite cartesian product of countable sets is countable?
here is the proof: http://planetmath.org/encyclopedia/ProductOfAFiniteNumberOfCountableSetsIsCountable.html
What is a binary function?
A binary function is a function f if there exists sets X, Y, and Z, such that f:X x Y -> Z where X x Y is the cartesian product of X and Y.
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.
Cartesian product of sets A and B is finite then does it follow that A and B are finite?
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.
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.
Prove that a finite cartesian product of countable sets is countable?
here is the proof: http://planetmath.org/encyclopedia/ProductOfAFiniteNumberOfCountableSetsIsCountable.html
What can you graph on a cartesian graph?
Any data consisting of two sets of quantitative measures on a set of objects. Although the horizontal axis is often used for categories, the graph is then not a Cartesian graph.Any data consisting of two sets of quantitative measures on a set of objects. Although the horizontal axis is often used for categories, the graph is then not a Cartesian graph.Any data consisting of two sets of quantitative measures on a set of objects. Although the horizontal axis is often used for categories, the graph is then not a Cartesian graph.Any data consisting of two sets of quantitative measures on a set of objects. Although the horizontal axis is often used for categories, the graph is then not a Cartesian graph.
What is two sets of data are plotted as ordered pairs in the coordinate plane?
The x and y coordinates are plotted on the Cartesian plane.
What is difference between Cartesian product and natural Join Operation?
Difference Between CARTESIAN PRODUCT & NATURAL JOINT Cartesian product is like the cross product ie every element of one row of one table/entity is multiplied to every column of another table for solving linked queries of two tables ... Where as natural Join is simply joining two or more entities eliminating the common attributes or columns.. @nayan answered it :)
What are the set of operation?
operation set
What is the definition of ordered pair in math?
An ordered pair is a pair of numbers, in cases where the order is relevant. Often used to indicate coordinates. Also, in general, to create new (larger) sets out of existing sets, in a process known as "Cartesian product"
What is a binary function?
A binary function is a function f if there exists sets X, Y, and Z, such that f:X x Y -> Z where X x Y is the cartesian product of X and Y.
