We explain what a set is and the types of set that exist. In addition, examples and the various meanings of this term.
What is set?
A set is defined as the grouping of different elements that share similar characteristics and properties with each other . These elements can be anything, such as numbers, songs, months, people, and so on.
In turn, a set can also become an element. For example, 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.
Types of sets
When forming a set, the way and how we group them together can vary, giving rise to different types of sets:
- Finite sets: The characteristic of this set is that its elements can be counted or enumerated in its entirety. For example, the months of the year establish a finite set: January, February, March, April, May, June, July, August, September, October, November and December.
- Infinite set : A set will be infinite when its elements are impossible to count or enumerate in its entirety, because they have no end. Numbers are a clear example of an infinite set.
- Unitary set : One that is composed of a single element. The moon is within this set, as it is the only natural satellite on planet earth.
- Empty set : it is a set which does not present or have elements.
- Homogeneous set : Sets whose elements have the same class or category.
- Heterogeneous set : The elements of these sets differ in class and category.
- Equivalent sets: Those sets whose quantity of elements is the same will be equivalent.
- Equal sets: Two or more sets may be said to be equal, when they are composed of identical elements.
The whole term in other fields
Despite using the general meaning that mathematics gives for the whole word, it can be used for other areas:
- Musical ensemble : This group will be called that containing two or more people who, through the voice or musical instrument, represent musical works with specific styles.
- Programming set : In programming , a group of different values is called a set, which do not have a specific order or duplicate values.
- Vocal ensemble : It is the group of people that interprets a musical work in a coordinated way.
- Numerical set : Grouping numbers through a series of structured properties.
- Instruction Set : is the name given to the white paper has instructions a CPU of computer can run.