Singleton Set Vs Empty Set
The table below gives us the difference between the singleton set and empty set.
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Singleton Set |
Empty Set |
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A set with only 1 element is called singleton set. |
A set with no element is called as empty set. |
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The cardinality of singleton set is one. |
The cardinality of empty set is zero. |
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Singleton set is also called as unit set. |
Empty set is also called as null set or void set. |
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Singleton set has two subsets: Empty Set and the Singleton Set itself. |
Empty set has only one subset i.e., Empty Set itself. |
Is Zero Set {0} a Singleton Set?
Zero set is a set with one element zero. The cardinality of zero set is 1. So, the zero set i.e., {0} is a singleton set. Zero set and null set are different as zero set represents a set with one element zero whereas the null set is a set with no elements. Since a set with one element is singleton set so, the zero set is also a singleton set.
Zero set S = {0} is a singleton set
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Singleton Set
Singleton set is a set with only one element. An example of a singleton set is an even prime number since there is only one prime number and all other primes are odd. Thus, the set of even prime numbers is a singleton set.
In this article, we will explore the singleton set, singleton set definition, singleton set symbol, singleton set examples, the cardinality of the singleton set, the power set of the singletons set, and others in detail.
Table of Content
- What is Singleton Set?
- Singleton Set Examples
- Cardinality of Singleton Set
- Power Set of a Singleton Set
- Properties of the Singleton Set
- Venn Diagram of a Singleton Set