Equivalence Relationship

Relationship that connects elements that are similar by one of their properties.

Relationship of a set E toward a set E that is reflexive, symmetric and transitive.

In the case of relationships between units of measurement, it is acceptable to use the symbol =. However, when reading them, it is preferable to use the expression "is equal to" or "is equivalent to".
So, for 1 m = 100 cm, we would say that one metre is equivalent to one hundred centimetres.

The relationship "...has the same parity as…" in the set of divisors of 64 is an equivalence relationship.
The relationship "...is parallel to…" in the set of lines on graph is an equivalence relationship.
The fractions [latex]\dfrac{6}{9}[/latex], [latex]\dfrac{10}{15}[/latex], [latex]\dfrac{14}{21}[/latex] and [latex]\dfrac{20}{30}[/latex] are equivalent, because they are all equivalent to the fraction [latex]\dfrac{2}{3}[/latex].
The units of measurement "1 m" and "100 cm" are equivalent units of measurement.
The relationship "…is perpendicular to…" in the set of lines on a graph is not an equivalence relationship.

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