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Definition: A relation on a set A is a subset C of the Cartesian product A x A. In other words, a relation is a set of ordered pairs with the first element of a pair from one set and the second element of a pair from a second set. It is often the case that the first and second set are the same, say X. In that case the relation is said to be over X.
Source: Topology (second edition) by James R. Munkres
Example: The < relation over the integers is the set of pairs (x,y) with x less than y.