Themes

# What is Finite Set/meaning/concept/elaboration

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.

### finite set

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.