It is said that something is equivalent to a different thing when between the two there is a certain similarity, equality or they have the same value. The adjective equivalent corresponds to the noun equivalence and in any of the contexts in which both terms are used it is possible to speak of a comparison between several things that present some degree of similarity.
Equivalence in mathematics
In the sphere of mathematics and logic, the concept of equivalent is expressed through the symbol =, which means that in a formulation with said symbol the parts involved have the same value. In order to carry out mathematical operations, it is necessary to take into account the equivalence relations, which are the relations between the elements of any set and their main characteristic is the implicit concept of equality. The importance of equivalence relations is that they divide the elements of a set into different classes, called equivalence classes (each element belongs to an exclusive class).
The principle of equivalence and its classes allow us to carry out everyday mathematical operations of all kinds, handle different units by applying the equivalence between the different measurement systems or calculate the value of one currency with respect to another, among many other possibilities.
The equivalent in other disciplines
When classifying and ordering the different kingdoms of nature, biologists study the characteristics of species and look for similarities between them, that is, how they are equivalent to each other. In this way, two different organs have equivalent functions between the male and female of the same species (for example, the ovaries and testes) or two respiratory systems of animals have equivalent functions (for example, the lung respiration of mammals and gill respiration of aquatic animals).
From a political and social point of view, each country has its own administrative organization and its own organisms and to understand them it is necessary to establish some type of equivalence or comparison.
In the field of language, the synonym is the phenomenon that expresses the equivalence between two words. In this case, that two words are synonymous does not mean that they are absolutely equivalent but that they are interchangeable even though they do not mean exactly the same thing.
If we analyze a human culture we find a series of elements (a language, some traditions and a certain history). To understand any cultural expression it is necessary to establish some type of equivalence with another cultural expression. From this approach it is appreciated that something that seems exclusive and different at first glance, is presented in another culture with a very similar sense and, therefore, they present an equivalence (for example, the different dance modalities, the rituals of each religion or different family models).