The language of mathematics allows us to explain and understand all kinds of reality . In order to know the different elements that make up something, one usually resorts to the so-called set theory. In this theory, terms such as the following are employed: universal set, empty, subset, infinite or finite.
All these concepts can be intuitively understood and do not need to be demonstrated.
A set is a group with several elements that share some common characteristic , such as the set of figures, numbers, mammals or people.
To represent the contents of a set, we can use a closed circle that contains all the elements integrated in each set modality.
All sets can be divided into two parts, finite and infinite. The first are those that contain a limited amount of elements, while the second are those that have a number of elements that cannot be counted. Logically, in every finite set, the elements that make it up are fully defined.
When a set is finite, the term cardinality is used, as it makes it possible to enumerate all its integrated elements. Thus, if the set A is formed by five elements, its cardinality is 5.
On the other hand, it is possible to refer to all elements of a finite set in two ways:
1) it can be done by extension when we mention all the elements one by one (for example, mention each one of the vowel letters that are integrated to the vowel set);
2) and by understanding when the general characteristic of all the elements that make up the set is expressed (for example, when I refer to all the vowels in the Spanish language I refer to each one of them, but I do not mention them individually) .
To name an element of a finite set, it is necessary to clearly know the content of a subject.
Thus, I can say that the five vowels constitute an ensemble, but that it cannot form a ensemble with the five best opera singers, since the idea of the best is subjective and, therefore, would not be valid.
Some finite sets can be subdivided into smaller parts or subsets. If we take the set A of all animals as a reference, we could speak of subset B formed by mammals or subset C formed by amphibians.