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What is a Cartesian product?

What is a Cartesian product? Here are some definitions.

Noun
  1. (set theory) The set of all possible pairs of elements whose components are members of two sets. Notation:
  2. (databases) All possible combinations of rows between all of the tables listed.
  3. (geometry) 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:
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