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Full Idea
Equivalence classes will 'partition' a set. That is, it will divide it into distinct subsets, according to each relation on the set.
Gist of Idea
We 'partition' a set into distinct subsets, according to each relation on its objects
Source
Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0)
Book Ref
Enderton,Herbert B.: 'A Mathematical Introduction to Logic' [Academic Press 2001], p.6