Difference Between Finite Sets and Infinite Sets
Finite sets are sets that can be put into one-to-one correspondence with any set of natural numbers. Infinite sets are sets that cannot be empty and cannot be put into one-to-one correspondence with any set of natural numbers. Example of a finite set: P = {5, 9, 11}. Example of infinite set X = {s, r, t, …}.
Characteristics |
Finite Set |
Infinite Set |
---|---|---|
Definition |
A set with a finite number of elements is called a finite set. |
The non-empty set that contains an infinite number of elements are called an infinite set. |
Mapping |
Finite sets can be mapped one-to-one with finite elements of the set of natural numbers. |
Only countable Infinite sets can be mapped one-to-one with a set of natural numbers, uncountable infinite sets can’t be mapped with natural numbers in a bijection. |
Cardinality |
Cardinality of finite sets = n Where n is the number of elements in the set. |
Cardinality of countably infinite set [N] = ℵ0 Cardinality of lowest uncountably infinite set [R] = ℵ1 |
Roaster Form |
It can be represented in Roaster form. | It cannot be represented in Roaster form. |
Example |
A = {3, 4} is a finite set. | A = {3, 4, …} is an infinite set. |
Also, Read
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