set

Knowledge

2022

We explain what a set is and the types of sets that exist. Also, examples and the various meanings of this term.

A set can also become an element.

What is a set?

A set is the grouping of different elements that share similar characteristics and properties. These elements can be subjects or objects, such as numbers, songs, months,persons, etc. For example: the set of prime numbers or the set of planets of the solar system.

In turn, a set can also become an element. For example: in the case of a bouquet of flowers, in principle a flower would be the first element, but the set of flowers can then be considered as a bouquet of flowers, thus becoming a new element.

To graph a set, brackets are used to delimit the elements that make it up, which are separated from each other by commas. For example: "S" is defined as the set of days of the week, therefore, S = [Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday].

See also:Database

Set theory

Set theory is the branch of math that studies sets. It was introduced as a discipline by the Russian mathematician Georg Cantor, who defined the set as the collection of finite or infinite elements and used it to explain mathematics.

Cantor studied the set of rational and natural numbers and his discovery of the sets of infinite numbers was revolutionary, since he revealed the existence of infinities of different sizes by ensuring that a greater infinite can always be found.

Cantor's discoveries were not well received in the mathematical realm of the late nineteenth century. However, today he is considered a visionary in the study of what he called the transfinites, a study that contributed to the study of abstract and infinite sets.

Types of sets

When forming a set, the way and the reason for the grouping of the elements that make it up can vary, giving rise to different types of sets, which can be:

  • Finite sets. Its elements can be counted or numbered in their entirety. For example: the months of the year, the days of the week or the continents.
  • Infinite set. Its elements cannot be counted or enumerated in their entirety, because they have no end. For example: the numbers.
  • Unitary set. It is made up of a single element. For example: The Moon is the only element in the set "natural satellites of the Earth".
  • Empty set. It does not present or contain elements.
  • Homogeneous set. Its elements have the same class or category.
  • Heterogeneous set. Its elements differ in class and category.

Regarding the relationship between sets, they can be:

  • Equivalent sets. The number of elements between two or more sets is the same.
  • Equal sets. Two or more sets are made up of identical elements.

Sets and subsets

It is called a subset to the set that is within another set, that is, the set A is a subset of the set B, if all the elements of A are included in B.

For example:

  • Mammals are a subset of the whole animal.
  • Odd numbers are a subset of the set of natural numbers.
  • The countries of South America are a subset of the countries of the world as a whole.
  • The spring months are a subset of the whole months of the year.
  • First graders are a subset of the set of children in school.

The term set in other fields

A vocal ensemble is the grouping of people who perform a musical work.

The word set is also used in other areas, such is the case of:

  • Musical ensemble. Group that contains two or more people who, through the voice or musical instruments, represent musical works.
  • Set inprogramming. Grouping of various values, which do not have a certain order or duplicate values.
  • Vocal ensemble. Grouping of people who perform a musical work in a coordinated way.
  • Numerical set. Grouping of numbers using a series of structured properties.
  • Instruction set. Grouping of instructions that aCPU fromcomputer can execute.
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