Examples of 'cartesian product' in a sentence
Meaning of "cartesian product"
In mathematics, the Cartesian product refers to the combination or union of two sets to create a new set. It is obtained by taking all possible ordered pairs, where the first element belongs to the first set and the second element belongs to the second set. The resulting set contains all possible combinations of elements from both sets. The Cartesian product is widely used in set theory, combinatorics, and algebraic structures
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- The set of all possible pairs of elements whose components are members of two sets. Notation: X×Y=(x,y)‖x∈X∧y∈Y.
- All possible combinations of rows between all of the tables listed.
- The set of points in an (m + n)-dimensional Cartesian space corresponding to all possible pairs of points from the two sets from spaces of dimension m and n. Notation: X×Y=(x_1,...x_m,y_1,...y_n)‖(x_1,...x_m)∈X∧(y_1,...y_n)∈Y.
How to use "cartesian product" in a sentence
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cartesian product
Any subset of such a cartesian product is called a relation.
Cartesian product operation was originally defined for simplicial sets.
This operation on morphisms is called cartesian product of morphisms.
Cartesian product of functions.
This is known as the cartesian product.
Cartesian product as a table.
We wish to show that the cartesian product of these sets is nonempty.
This follows from the formula for the cardinality of the cartesian product of sets.
The Cartesian product of two complex manifolds.
The product in this category is given by the cartesian product of sets.
We return Cartesian product of the n resulting intervals.
Applications are given in algebra and combinatorics to group actions that preserve cartesian product structures.
Relation is a subset of a Cartesian product of list domains.
The Cartesian product is also not associative.
A relation is a set that is a subset of a Cartesian product.
See also
A join is a Cartesian product with an applied restriction.
A relation is defined on a SOD as a subset of its cartesian product.
The Cartesian product is a direct product of sets.
We have defined the Cartesian product of two sets.
The Cartesian product is also commutative and associative.
We now define a relation as a subset of the Cartesian product.
This generalizes the Cartesian product in the category of sets.
A Cartesian product is bipartite if and only if each of its factors is.
Which is a subset of the Cartesian product.
The Cartesian product of any family of nonempty sets is nonempty.
A common operation that generates tuples is the Cartesian product.
The Cartesian product of two curves also provides examples.
This is an operation that produces the Cartesian product of two tables.
The Cartesian product of a finite set of finite sets is finite.
It is the union of the Cartesian product and the tensor product.
A Cartesian product is vertex transitive if and only if each of its factors is.
A table can be created by taking the Cartesian product of a set of columns.
The Cartesian product of two median graphs is another median graph.
The second construction involves the Cartesian product of two topological spaces.
The Cartesian product of graphs is not a product in the sense of category theory.
Compare this to the notation for the Cartesian product of a family of sets.
The Cartesian product of any finite set of partial cubes is another partial cube.
The product in Top is given by the product topology on the Cartesian product.
The from clause by itself defines a Cartesian Product of the relations in the clause.
A correspondence between two sets and is any subset of the Cartesian product.
They are exactly the graphs whose Cartesian product with a single edge remains perfect.
A binary relation on a set S is a subset of the Cartesian product.
The cartesian product is implemented in SQL as the Cross join operator.
Then he defines a product space to be any finite Cartesian product of these underlying spaces.
Cartesian product graphs can be recognized efficiently, in linear time.
All three can similarly be defined for the Cartesian product of more than two sets.
In topology, the cartesian product of topological spaces can be given several different topologies.
It is a binary operation that allows combining certain selections and a Cartesian product into one operation.
Nullary Cartesian product.
Formally, relations are a subset of the cartesian product.
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