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Definition: An equivalence relation on a set A is a relation C on A having the following three properties: 1) (Reflexivity) xCx for every x in A. 2) (Symmetry) If xCy, then yCx. 3) (Transitivity) If xCy and yCz, then xCz.
Source: Topology (second edition) by James R. Munkres
Example: Over the integers, the relation x = y mod 10 is an equivalence relation.