What is the Cartesian product?

In mathematics, a Cartesian product refers to an operation between two or more sets that combines the elements of these sets into the form of an ordered pair, for example, if there are two Set A={a,b} and B={1,2}, then their Cartesian product is {(a,1),(a,2),(b,1),(b,2)}.

In mathematics, the Cartesian product refers to an operation between two sets (or more sets) that combines these sets The elements in are combined into ordered pairs. For example, if there are two sets A={a,b} and B={1,2}, then their Cartesian product is {(a,1),(a,2),(b,1),( b,2)}.

Normally, if there is a Cartesian product of n sets A1, A2,...,An, then it contains all elements of the form (a1, a2,...,an), where a1∈A1, a2∈A2,…,an∈An.

Cartesian product is widely used in combinatorial mathematics, discrete mathematics, computer science and other fields. For example, in a relational database, the Cartesian product can be used to describe a join operation between two tables, which combines all the data in the two tables and generates a new table. In computer science, the Cartesian product can also be used to describe the index calculation of multi-dimensional arrays, as well as the iterative process in certain algorithms.

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