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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.
