Cartesian Product

Given two sets A and B, the Cartesian product, also known as the cross product or even just product, is written as A x B, which is read as “A cross B.” It is the set of all ordered pairs (a, b) where a \in A and b \in B.

A x B = \{(a, b) | a \in A~and~b \in B\}

When a set is crossed with itself one or more times it is written A^n. For example, A^2 is usually written instead of A x A.

Euclidean three-space, \mathbb{R}^3, is a very common Cartesian product.

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