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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.
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 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.
Prove that a finite cartesian product of countable sets is countable?
here is the proof: http://planetmath.org/encyclopedia/ProductOfAFiniteNumberOfCountableSetsIsCountable.html
How do you find the center and radius with an equation not in standard form?
By using Cartesian equations for circles on the Cartesian plane
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.
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 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 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.
How does the magnitude of a vector relate to the dot product?
The magnitude of dot product of two vectors is equal to the product of first vector to the component of second vector in the direction of first. for ex.- A.B=ABcos@
Is the Cartesian coordinates a scalar or a vector or neither?
A vector is a magnitude with a direction, so if you have a line that is +2 on the x-axis and +2 on the y-axis, that would be a vector.
Is a cartesian plane the same as a cartesian coordinate?
The cartesian coordinates are plotted on the cartesian plane
Prove that a finite cartesian product of countable sets is countable?
here is the proof: http://planetmath.org/encyclopedia/ProductOfAFiniteNumberOfCountableSetsIsCountable.html
What is the value of scalar product of two vectors A and B where value of vector A and B is not zero and vector product of two vectors A and B is not zero?
Scalar product = (magnitude of 'A') times (magnitude of 'B') times (cosine of the angle between 'A' and 'B')
What is magnitude of their initial momentum?
The magnitude of their initial momentum depends on the mass and velocity of the objects in question. It is calculated as the product of mass and velocity.
What is formula of a works?
it is the dot product of displacement and force . i.e. Fdcos(A) where F is the magnitude of force , d is the magnitude of displacement and A is the angle between them
