Genetic itinerary of equivalence relations in school and daily life

Abstract

The concept of equivalence relation describes the prolonged practice of man with himself and with society, that is to say, it marks a passage from the singular to the plural, a search among objects or concepts that possess some kind of correspondence in order to then classify them as equivalent or non-equivalent. The equivalence relations are a cultural product that has accompanied man in his different historical stages, but that becomes invisible most of the time because of its everyday life, therefore, there are different mathematical concepts, which are isolated by the fact of not evidencing their applicability in daily life. Another essential aspect about equivalence relations is that they are essential mechanisms to understand the functionality or behavior of different things that are conjugated in their similarities or that from their differences show aspects that allow the definition of a certain type of relation. In this sense and under the philosophy of showing an itinerary of the concept of equivalence relation, detailed exemplifications are presented in diverse contexts and educational levels, as well as the corresponding determination of: equivalence classes and quotient set.