A **relation** is between two given sets. So a relation *R* between set *A* and a set *B* is a subset
of their cartesian product:

- $ 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:

- reflexivity
- symmetry
- transitivity

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.

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