A set (from the Latin coniunctus) is what is united, contiguous or incorporated with something else, or that is mixed, combined or allied with something else different. A set, therefore, is an aggregate of several things or people.
For example: “Help me load that set of boxes into the truck”, “In this country, the political parties are groups of thieves and swindlers”, “The fight ended when a group of police officers showed up and ordered the dispersal of the present ”.
According to abbreviationfinder.org, the totality of the elements that have a common property that distinguishes them from others is also known as a set: “Today we are going to work with the set of prime numbers”, “The set of vowels is simpler than the set of consonants ”.
Another use of the concept of ensemble points to the group of people who perform singing, playing musical instruments and / or dancing : “My dream is to play in a rock ensemble”, “Historically, English rock ensembles have always achieved more success at the level. international than the North Americans ”. In a similar sense, the players of the same team are part of a team: “The white-and-blue team prevails two to one over its rival. “
The game dress women, finally, also called set: “For my birthday, my husband gave me a set of jacket and pants”.
In the field of mathematics, a set points to all the entities that have a common property. A set is made up of a finite or infinite number of elements, the order of which is irrelevant. Mathematical sets can be defined by extension (listing all its elements one by one) or by comprehension (only one characteristic common to all elements is mentioned).
It was only in the early nineteenth century that scientists began to use the concept of set, coinciding with advances in the study of infinity. The mathematicians Bolzano and Riemann, two people whose contributions are still indispensable today, used abstract sets to express their ideas.
One can also mention the work of Dedekind, another pioneer who bequeathed important foundations to modern algebra, with a conjunctist point of view ; Among the concepts on which he worked we can mention the partitions (families of subsets of a given set), the morphisms (functions that relate two mathematical objects while preserving their structure) and the equivalence relations (they serve to find certain elements of a set that have common characteristics or properties).
However, the author of set theory, studied as an independent discipline, was the German mathematician Georg Cantor, who investigated with particular devotion the sets of infinite numbers and their properties.
It is possible to perform certain basic operations that allow finding sets within others:
union : it is symbolized with a kind of U, and it is the set formed by the elements that belong to any of the sets that are proposed for union (in the case of A and B, the resulting set will be A U B);
intersection : its symbol is similar to a U rotated 180 ° and allows finding the elements that the given sets have in common;
difference : starting from the sets A and B, their difference will be the set A \, formed by the elements that are only found in A;
complement : if a set U contains one of name A, then the complement of the latter will be the one that contains the elements that do not belong to A;
symmetric difference : its symbol is a triangle and represents the set of elements that belong only to one of two given sets;
Cartesian product : the set A x B is the Cartesian product of A and B, and it is obtained with ordered pairs of an element of A followed by one of B (a, b).