What are the differences between finite sets and infinite sets?
Finite set: A set is said to be a finite set if it is either void set or the process of counting of elements surely comes to an end is called a finite set.
In a finite set the element can be listed if it has a limited i.e. countable by natural number 1, 2, 3, ……… and the process of listing terminates at a certain natural number N.
The number of distinct elements counted in a finite set S is denoted by n[S]. The number of elements of a finite set A is called the order or cardinal number of a set A and is symbolically denoted by n[A].
Thus, if the set A be that of the English alphabets, then n[A] = 26: For, it contains 26 elements in it. Again if the set A be the vowels of the English alphabets i.e. A = {a, e, i, o, u} then n[A] = 5.
Note:
The element does not occur more than once in a set.
Infinite set:
A set is said to be an infinite set whose elements cannot be listed if it has an unlimited [i.e. uncountable] by the natural number 1, 2, 3, 4, ………… n, for any natural number n is called a infinite set.
A set which is not finite is called an infinite set.
Now we will discuss about the examples of finite sets and infinite sets.
Examples of finite set:
1. Let P = {5, 10, 15, 20, 25, 30}
Then, P is a finite set and n[P] = 6.
2. Let Q = {natural numbers less than 25}
Then, Q is a finite set and n[P] = 24.
3. Let R = {whole numbers between 5 and 45}
Then, R is a finite set and n[R] = 38.
4. Let S = {x : x ∈ Z and x^2 – 81 = 0}
Then, S = {-9, 9} is a finite set and n[S] = 2.
5. The set of all persons in America is a finite set.
6. The set of all birds in California is a finite set.
Examples of infinite set:
1. Set of all points in a plane is an infinite set.
2. Set of all points in a line segment is an infinite set.
3. Set of all positive integers which is multiple of 3 is an infinite set.
4. W = {0, 1, 2, 3, ……..} i.e. set of all whole numbers is an infinite set.
5. N = {1, 2, 3, ……….} i.e. set of all natural numbers is an infinite set.
6. Z = {……… -2, -1, 0, 1, 2, ……….} i.e. set of all integers is an infinite set.
Thus, from the above discussions we know how to distinguish between the finite sets and infinite sets with examples.
● Set Theory
●Sets Theory
● Representation of a Set
●Types of Sets
● Finite Sets and Infinite Sets
●Power Set
● Problems on Union of Sets
●Problems on Intersection of Sets
● Difference of two Sets
●Complement of a Set
● Problems on Complement of a Set
●Problems on Operation on Sets
● Word Problems on Sets
●Venn Diagrams in Different Situations
● Relationship in Sets using Venn Diagram
●Union of Sets using Venn Diagram
● Intersection of Sets using Venn Diagram
●Disjoint of Sets using Venn Diagram
●Difference of Sets using Venn Diagram
● Examples on Venn Diagram
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.