Introduction to Finite Math Problems
Finite set:
The number of elements one by one in a set A. If it comes to an end of process, then the set A is said to be a finite set.
Infinite Set:
If we never come to an end in counting the elements, then the set A is said to be an infinite set.
Cardinal Number:
The number of elements in a set A is called the cardinal number of the set A and is denoted by the symbol n(A) which is read as the number of elements in the set A.
if A is a finite set, then n(A) is a whole number.
Finite Sets
Some of the finite sets are show in the following
A = {x | x ?W, x < 5}.
{All schools in Tamil Nadu}.
{Students in IX standard in your school}.
Solution:
1. x ?W, x < 5 ? x = 0, 1, 2, 3, 4.
? A = {0, 1, 2, 3, 4}. When we count elements of A one by one as 1 for 0, 2 for 1, 3 for 2, 4 for 3, 5 for 4, we come to an end .
Therefore n(A) = 5 and so A is a finite set.
2. All schools in Tamil Nadu can be counted one by one and we come to an end in the counting process. So the set {All schools in Tamil Nadu} is a finite set.
3. When we count the students of IX standard in your school, we come to an end in the counting process. So the set {Students in IX standard in your school} is a finite set.
Infinte Sets
Some of the infinite sets are show in the following
N.
W.
Z.
The set of all prime numbers.
Solution:
N = {1, 2, 3,…}. When we count elements of N one by one as 1 for 1, 2 for 2, 3 for 3, 4 for 4, we are not able to come to an end in the counting process.
Therefore the set N is an infinite set.
W = {0, 1, 2, 3,…}. When we count elements of Wone by one as 1 for 0, 2 for 1, 3 for 2, 4 for 3, we are unable to come to an end in the counting process. ? the set W is an infinite set.
Z = {0, 1, -1, 2, -2,…}. When we count elements of Z one by one as 1 for 0, 2 for 1, 3 for -1, 4 for 2, 5 for -2 and so on, we are not able to come to an end in the counting process. ? the set Z is an infinite set.
When we write the prime numbers one by one as 2, 3, 5, 7, 11, 13, 17 and so on, we are unable to come to an end in the counting process.
Therefore the set of all prime numbers is an infinite
Finite set:
The number of elements one by one in a set A. If it comes to an end of process, then the set A is said to be a finite set.
Infinite Set:
If we never come to an end in counting the elements, then the set A is said to be an infinite set.
Cardinal Number:
The number of elements in a set A is called the cardinal number of the set A and is denoted by the symbol n(A) which is read as the number of elements in the set A.
if A is a finite set, then n(A) is a whole number.
Finite Sets
Some of the finite sets are show in the following
A = {x | x ?W, x < 5}.
{All schools in Tamil Nadu}.
{Students in IX standard in your school}.
Solution:
1. x ?W, x < 5 ? x = 0, 1, 2, 3, 4.
? A = {0, 1, 2, 3, 4}. When we count elements of A one by one as 1 for 0, 2 for 1, 3 for 2, 4 for 3, 5 for 4, we come to an end .
Therefore n(A) = 5 and so A is a finite set.
2. All schools in Tamil Nadu can be counted one by one and we come to an end in the counting process. So the set {All schools in Tamil Nadu} is a finite set.
3. When we count the students of IX standard in your school, we come to an end in the counting process. So the set {Students in IX standard in your school} is a finite set.
Infinte Sets
Some of the infinite sets are show in the following
N.
W.
Z.
The set of all prime numbers.
Solution:
N = {1, 2, 3,…}. When we count elements of N one by one as 1 for 1, 2 for 2, 3 for 3, 4 for 4, we are not able to come to an end in the counting process.
Therefore the set N is an infinite set.
W = {0, 1, 2, 3,…}. When we count elements of Wone by one as 1 for 0, 2 for 1, 3 for 2, 4 for 3, we are unable to come to an end in the counting process. ? the set W is an infinite set.
Z = {0, 1, -1, 2, -2,…}. When we count elements of Z one by one as 1 for 0, 2 for 1, 3 for -1, 4 for 2, 5 for -2 and so on, we are not able to come to an end in the counting process. ? the set Z is an infinite set.
When we write the prime numbers one by one as 2, 3, 5, 7, 11, 13, 17 and so on, we are unable to come to an end in the counting process.
Therefore the set of all prime numbers is an infinite
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