Sets are categorized into four types based on the number of elements it contain. In this chapter, we will discuss in detail all four types of sets and analyze their definitions and examples.
Summary
- Set is a well-defined collection of distinct objects.
- On the basis of the number of elements, sets are categorized into four types.
Types of Sets
There are four types of sets on the basis of their cardinality number. Those sets are:
- Null Set
- Unit Set
- Finite Set
- Infinite Set
Null Set
Null Set is also known as an empty set. It is a set in which there are no elements. In other words, a set having no distinct elements is said to be an empty or a null set. A null set can also be represented by a ‘$\phi$‘ (phi) symbol. Or, it is also represented by ‘{}‘ (open and close braces with no spaces in between).
For example: A set of boys present in a girls’ hostel. The set mentioned here is null or empty. It is because there can be no boys in a girls’ hostel.
Another example is a set of mountains present in the Lumbini province of Nepal. This set is also null because there are no mountains in Lumbini province.
From the above two examples, we can understand that a set that has no actual meaning, in general understanding, is said to be a null set. Such sets must not have any known or distinct element present within them.
Unit Set
Unit Set is also known as singleton set. It is a set consisting of a single element. In other words, a set having only one element is said to be a unit or singleton set.
For example: A set of real numbers between 2 and 4. The set mentioned here is a unit or singleton set. It is because there is only one real number between 2 and 4 i.e. 3.
Second example: A = { $\phi$ } is a unit set. This is because it has only a single element. Here, '$\phi$' doesn’t represent a null set rather it acts as an element of set A.
Another example is a set of planets in the solar system where humans are living now. This set is also a unit set because the answer is The Earth only. At present, there is only one planet capable of human existence in the solar system.
From the above two examples, we can understand that a set that only has a particular and a single element, in general understanding, is said to be a unit set.
Finite Set
Finite Set is a set consisting of finite number of elements. In other words, a set that has countable number of elements is known as a finite set.
Any set that has limited number of elements is a finite set. Null sets and Unit sets are also finite set.
For example: A set of first 500 multiples of 5. The elements of this set are 500. Though they are a lot but we can count them and the elements have a start and a end point. Thus, this set is a finite set.
Another example: B = {a,e,i,o,u}. Set B is a finite set because it has five elements only.