general

set definition

A set is the grouping, class, or collection of objects or, failing that, of elements that belong to and correspond to the same category or group of things, that is why they can be grouped in the same set. This belonging relationship that is established between objects or elements is absolute and possibly discernible and observable by anyone. Among the objects or elements capable of integrating or forming a set are of course physical things, such as tables, chairs and books, but also by abstract entities such as numbers or letters.

Sets are a subject of study in mathematics and surely most of those who are reading the review on the term have learned what they know about them in the hours of mathematics in school.

Some basic considerations to take into account when dealing with sets is that they can be determined in two ways: by extension and understanding. By extension when the components of a set A containing natural numbers less than 8 are described one by one, for example: A = {1,2,3,4,5,6,7}. And it is said that it is determined by understanding when only a common characteristic is listed that all the elements that compose it gather. For example: set A is made up of primary colors A = {red}. It can also be that two sets are equal to each other because they share all the elements that compose them.

Traditionally, to describe the elements that make up a set, braces are opened and, if necessary, since they are more than one element, they are separated through the use of commas.

When representing the sets, we may find ourselves in the following situations: union, which is the set of all the elements contained in at least one of them; the intersection that implies meeting in the same set of all those elements that are repeated or share a pair of sets. The first is represented with the two sets united and painted the same color, marking that union and in the second case the union of the middle of these two sets is painted as common, which is where the same elements congregate.