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Every class of equivalence is a set as well (a subset of A), so it is possible to continue with the partition procedure applied on that particular subset, by using some other relation of equivalence. For example, the footprints divided according to the kind of animal that produced them it is possible to subdivide according to the size of footprints. Applying several relations of equivalence (in recursion) to the complete set A we obtain the classification. In opposite, singular elements have no equivalents: they are equivalent only to themselve and nothing else.

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