The language of mathematics allows us to explain and understand all kinds of realities. To know the diverse elements that make up something, the so-called set theory is normally used. In this theory, terms such as the following are used: universal, empty, subset, infinite or finite set.
All of these concepts can be understood intuitively and do not need to be demonstrated.
A set is a group of diverse elements that share some characteristic in common, such as the set of figures, numbers, mammals or people.
To represent the content of a set we can use a closed circle that contains all the elements integrated in each set modality.
Finite set
All sets can be divided into two sections, the finite and the infinite. The former are those that contain a limited number of items and the latter are those that have a number of items that cannot be counted. As is logical, in every finite set the elements that form it are totally defined.
When a set is finite, the term cardinality is used, since it is possible to list all the elements integrated in it. Thus, if set A is made up of five elements, its cardinality is 5.
On the other hand, it is possible to refer to all the elements of a finite set in two ways:
1) is done by extension when we mention all the elements one by one (for example, we mention each of the vowel letters that are integrated in the set of vowels) and
2) It is done by understanding when the general characteristic of all the elements that make up the set is expressed (for example, if I refer to all the vowels of the Spanish language, I mean each of them but I am not mentioning them individually) .
To name an element of a finite set it is necessary that the content of a subject be clearly known
Thus, I can say that the five vowels constitute an ensemble, but I could not form an ensemble with the five best opera singers, since the idea of best is subjective and, therefore, would not be valid.
Some finite sets can be subdivided into minor parts or subsets. If we take as a reference set A on all animals, we could speak of subset B formed by mammals or subset C formed by amphibians.
Photos: Fotolia - Satika / Alexander Limbach
