Solved Examples on Infinite Sets
Example 1: Check whether the given sets are finite or infinite.
(i) A = {3, 6, 9, …}
(ii) B = {1, 2}
(iii) X = {a, b, c, …}
Answer:
(i) A = {3, 6, 9, …}
A is an infinite set.
(ii) B = {1, 2}
The number of elements in B is 2 which is finite. So, B is a finite set.
(iii) X = {a, b, c, …}
X is an infinite set.
Example 2: Check whether the given sets are finite or infinite.
(i) Z = {15, 19, 21, 45}
(ii) P = {“infinite”, “set”, …}
(iii) Q = {…, p, q, r, s, …}
Answer:
(i) Z = {15, 19, 21, 45}
The number of elements in Z is 4 which is finite. So, Z is a finite set.
(ii) P = {“infinite”, “set”, …}
P is an infinite set as it does not have end point.
(iii) Q = {…, p, q, r, s, …}
Q is an infinite set as it does not have start and end point.
Example 3: Check whether the given sets are finite or infinite.
(i) Factors of 25
(ii) Multiples of 2
(iii) Lines segments in a plane
Solution:
(i) Factors of 25
There are only 3 factors of 25 ( 1, 5 and 25). So, the set of factors of 25 is finite set.
(ii) Multiples of 2
Multiples of 2 are {1, 2, 4, 6, …}
There is no end point for the set of multiples of 2. So, the set multiples of 2 is infinite set.
(iii) Lines segments in a plane
There can be uncountable line segments in a plane. So, the set of line segments in a plane is an infinite set.
Example 4: Proof the power set of set A = {2, 3, 5, …} is an infinite set.
Solution:
A = {2, 3, 5, …} is an infinite set.
From the property of infinite set, we know that power set of infinite set is infinite.
So, power set of A is an 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