Types of Infinite Sets
Infinite Sets are classified into two categories that are:
- Countable Infinite Set
- Uncountable Infinite Set
Countable Infinite Set
A set X is called a countable infinite set if and only if set A has the same cardinality as N (natural numbers). Some examples of countable infinite sets are a set of natural numbers N, a set of integers Z, etc.
Note: (Countable Set) A set is countable if and only if it is finite or countable infinite.
Uncountable Infinite Set
A set which can’t be mapped to the set of natural number is called the Uncountable Infinite Set. We can also say that, an uncountable infinite set is a set that is not countable. The set of real numbers R is one of the examples of an uncountable infinite set.
Infinite Set
Infinte set is one of the types of Sets based upon the cardinality in Set Theory and sets are one of the important topics in mathematics. In simple words, an infinite set is a set with infinite elements i.e., the number of elements in an infinite set never depletes. This concept of infinite sets seems to be complicated at first sight but we’ll try our best to make it as comprehensive and understanding as possible.
This article deals with this concept and tries its best to explain the concept in detail. Other than that, this article covers definition, notation, types, cardinality, examples, and properties of Infinite Sets. So, let’s start learning about Infinite Sets.
Table of Content
- What are Infinite Sets?
- Infinite Sets Definition
- Infinite Set Notation
- Infinite Set Examples
- Types of Infinite Sets
- Properties of Infinite Sets
- Venn Diagram for Infinite Sets
- Difference Between Finite Sets and Infinite Sets