- $ R\subseteq A\times B $
An equivalence relation in a set A is a relation $ R\subseteq A\times A $ i.e. an endo-relation in a set, which obeys the conditions:
An example of this is a sum fractional numbers. Here a rational number can be represented as several different fractions with different denominators, so by making the fractions have a common denominator we can simplify the addition.