We explain what a set is and the types of sets that exist. Also, examples and the various meanings of this term.
What is a set?
a set It is the grouping of different elements that share similar characteristics and properties. . These elements can be subjects or objects, such as numbers, songs, months, people, etc. For example: the set of prime numbers or the set of planets in 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, square 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).
set theory
set theory It is the branch of mathematics 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 sets of infinite numbers was revolutionary. since he revealed the existence of infinities of different sizes by ensuring that a larger infinity can always be found.
Cantor's discoveries were not well received in the mathematical field of the late 19th century. However, today he is considered a visionary in the study of what he called transfinites, a study that contributed to that of abstract and infinite sets.
Types of sets
When forming a set, the way and why the elements that make it up are grouped can vary, giving rise to different types of sets, which can be:
- Finite sets. Its elements can be counted or listed 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: numbers.
- Unitary set. It is made up of a single element. For example: The Moon is the only element in the set of “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 composed of identical elements.
Sets and subsets
A subset is called set that is inside another set, that is, set A is a subset of set B, if all the elements of A are included in B.
For example:
- Mammals are a subset of the group of animals.
- Odd numbers are a subset of the set of natural numbers.
- The countries of South America are a subset of all the countries of the world.
- The spring months are a subset of the set of months of the year.
- First graders are a subset of the school's set of children.
The term joint in other fields
The word set is also used in other areas, such as:
- Musical ensemble. Group that contains two or more people who, through voice or musical instruments, represent musical works.
- Set in programming. Grouping of various values, which do not have a specific order or duplicate values.
- Vocal ensemble. Group of people who perform a musical work in a coordinated manner.
- Numerical set. Grouping numbers using a series of structured properties.
- Instruction set. A group of instructions that a computer CPU can execute.
References
- “Georg Cantor, the man who discovered different infinities” in Open Mind –BBVA.
- “Set theory” in Britannica.
- “Set theory” in Stanford Encyclopedia of Philosophy.
- “The terrible dynasty of transfinite numbers” in El País.
