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What is a relation?

What is a relation? Here are some definitions.

Noun
  1. The manner in which two things may be associated.
  2. A member of one's family.
  3. The act of relating a story.
  4. (set theory) A set of ordered tuples.
  5. (set theory) Specifically, a set of ordered pairs.
  6. (databases) A set of ordered tuples retrievable by a relational database; a table.
  7. (mathematics) A statement of equality of two products of generators, used in the presentation of a group.
  8. (category theory) A subobject of a product of objects.
  9. (usually collocated: sexual relation) The act of intercourse.
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