The concept of a set is used when trying to define a class, elements, conglomerate and similar meanings , which make it up. The same and depending on the area in question, has different connotations, as we will see later in the classification.
It is a factor of integration of the elements within the same group, thus giving a unique value to both the parts and the whole. Within the elements that can appear in the groups we have physical objects, abstract elements, letters, numbers and other grouping possibilities.
The set, as an integrating element of a certain group, has as its main property the duty to be well planned to give a foundation to the parts that make up the group, that is, if there really is a value of group membership of said element.
Types of sets in mathematics:
Within the sciences of mathematics, the total factor of the elements that make up the group and have common characteristics or values within the same group is called a set. These sets are made up of a finite or infinite number depending on the property of said group where the organization may or may not be important.
Said mathematical sets can be classified depending on the group value, that is, it can be called by its extension where the number of elements of the group is defined, or by its understanding, that is, referring to the property in question of part of the elements. group elements.
It is thus defined when in the group each of the elements that compose it has the same values, this is used when a certain problem is being analyzed and the elaboration of a subdivision of subsets is required to explain the purpose of the study.
Historically, in antiquity, the universal set was defined as the one that allowed grouping all kinds of objects or ideas. At present and thanks to the philosophy of science and science itself, it has been possible to determine categories that allow the creation of large subsets.
For example, if what is intended is to develop sets where the basic property is the use of letters, the result as a universal set would be the alphabet itself.
If the statement of the problem being analyzed has to do with numbers, then the universal set would be, for example, the natural numbers.
It is the type of set in which precisely some type of element does not exist. This type serves to support a reflection that starts from the structure of logic.
This type of set has as its main characteristic the fact that it only has one unit or one single element.
This type of grouping can be recognized from the number of elements that make it up in a quantifiable way, that is, there is a limit to the sequence and number of elements that make it up and therefore it is measurable.
Contrary to the previous concept, in this case the number of elements that make it up cannot be measurable, and the way in which this type of group is defined or determined is through understanding through knowledge or naming of the qualities that they have the elements that make it up that allow defining the total set.
They are those groups that within their elements are only numbers, which propose a number of structural-type characteristics with specific properties. Among them we have the following: they provide values to develop algebraic operations, they give a sense of order to the things that are listed, they develop values or equivalence connections; among other applications.
They are those groups that present a similarity in terms of the number of elements that make up precisely said group, that is, there is an equivalence in the cardinal number of elements on both sides.
They have as a defining factor the fact that the elements that confirm the group have the same characteristic. This, when joining with another group with similar characteristics, allows another unit to be generated without generating incompatibility, allows one or more subsets to form a larger set.
Non-convex or disjunctive set
Contrary to the previous concept, in this case there is no element of similarity or equality with respect to each element, so the empty set can be given by joining several subgroups.
It seeks to comply with the basic property that is that the parts that make up the group can relate to each other without losing the unit of value in its entirety.
It represents the opposite case of the previous concept, that is, they are those elements that, due to their unit value, cannot be linked with the other elements of the group, although due to other properties or needs they can be grouped together.