A musical band could be mentioned as an ensemble.
Set (from Latin coniunctus ) is that which is united, contiguous or incorporated with another thing , or that is mixed, combined or allied with another diverse thing . 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, political parties are groups of thieves and scammers,” “The fight ended when a group of police officers showed up and ordered the dispersion of the present.”
The totality of elements that have a property in common 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.”
The ensemble as a musical or sports group and as a dress-up game
Another use of the concept of ensemble indicates the group of people who act by 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 an international level.” international than the North Americans . In a similar sense, the players of the same team are part of a team: “The blue and white team wins two to one over its rival.”
The feminine dressing game is also called an outfit: “For my birthday, my husband gave me a jacket and pants set.”
The idea of a set is frequently used in the field of mathematics.
The notion in mathematics
In the field of mathematics , a set indicates the totality of entities that have a common property. A set is made up of a finite or infinite number of elements, whose order 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 at the beginning of the 19th century that scientists began to use the concept of a 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.
We can also mention the work of Dedekind, another pioneer who bequeathed important foundations to modern algebra , with a set point of view ; Among the concepts on which he worked we can mention partitions (families of subsets of a given set), morphisms ( functions that relate two mathematical objects while preserving their structure) and 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 sets of infinite numbers and their properties with particular devotion.
Operations with sets
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 us to find the elements that the given sets have in common;
difference : starting from sets A and B, their difference will be set A , formed by the elements that are only found in A;
complement : if a set U contains one with the 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 to only one of two given sets;
Cartesian product : The set A x B is the Cartesian product of A and B, and is achieved with ordered pairs of an element of A followed by one of B (a, b).