“Cartesian product”的概念、定义、翻译、参考文献-科学参考

Cartesian product

Mathematics

The Cartesian product A×B, of sets A and B, is the set of all ordered pairs (a, b), where a ∈ A and b ∈ B. More generally, for sets A₁, A₂,…, A_n, the Cartesian product A₁×A₂×…×A_n can be defined as the set of ordered n-tuples (a₁,a₂,…,a_n) where a_i ∈ A_i for each i.

The Cartesian product $A \times B$

Computer

of two sets S and T. The set of all ordered pairs of the form (s,t) with the property that s is a member of S and t is a member of T; this is usually written as S × T. Formally,
$S \times T = {(s, t) | (s \in S) and (t \in T)}$
If R denotes the set of real numbers, then R × R is just the set of points in the (Cartesian) plane or it can be regarded as the set of complex numbers, hence the name.
The concept can be extended to deal with the Cartesian product of n sets,
$S_{1}, S_{2}, \dots, S_{n}$
This is the set of ordered n-tuples
$(s_{1}, s_{2}, \dots, s_{n})$
with the property that each s_i is in S_i. In the case where each S_i is the same set S, it is customary to write S ⁿ for
$S \times S \times \dots S (n terms)$

Philosophy

The Cartesian product of two sets, A and B (written A × B), is the set of all ordered pairs whose first member is an element of A, and whose second member is an element of B.

单词	Cartesian product
释义	Cartesian product Mathematics The Cartesian product A×B, of sets A and B, is the set of all ordered pairs (a, b), where a ∈ A and b ∈ B. More generally, for sets A₁, A₂,…, A_n, the Cartesian product A₁×A₂×…×A_n can be defined as the set of ordered n-tuples (a₁,a₂,…,a_n) where a_i ∈ A_i for each i. The Cartesian product $A \times B$ Computer of two sets S and T. The set of all ordered pairs of the form (s,t) with the property that s is a member of S and t is a member of T; this is usually written as S × T. Formally, $S \times T = {(s, t) \| (s \in S) and (t \in T)}$ If R denotes the set of real numbers, then R × R is just the set of points in the (Cartesian) plane or it can be regarded as the set of complex numbers, hence the name. The concept can be extended to deal with the Cartesian product of n sets, $S_{1}, S_{2}, \dots, S_{n}$ This is the set of ordered n-tuples $(s_{1}, s_{2}, \dots, s_{n})$ with the property that each s_i is in S_i. In the case where each S_i is the same set S, it is customary to write S ⁿ for $S \times S \times \dots S (n terms)$ Philosophy The Cartesian product of two sets, A and B (written A × B), is the set of all ordered pairs whose first member is an element of A, and whose second member is an element of B.
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