(ii) Let ‘S’ be the set of solutions of the equation x
2
– 16 = 0. Then S is finite.
(iii) Let ‘G’ be the set of points on a line. Then G is infinite.
Example-13.
State which of the following sets are finite or infinite.
(i) {x : x ∈ N and (x - 1) (x - 2) = 0} (ii) {x : x ∈ N and x
2
= 4}
(iii) {x : x ∈ N and 2x - 2 = 0} (iv) {x : x ∈ N and x is prime}
(v) {x : x ∈ N and x is odd}
solution:
(i) x can take the values 1 or 2 in the given case. The set is {1,2}. Hence, it is finite.
(ii) x
2
= 4, implies that x = +2 or -2. But x Î ¥ or x is a natural number so the set
is{2}. Hence, it is finite.
(iii) In a given set x = 1 and 1 ∈ N . Hence, it is finite.
(iv) The given set is the set of all prime numbers. There are infinitely many prime
numbers. Hence, set is infinite.
(v) Since there are infinite number of odd numbers, hence the set is infinite.
2.9 CARDINALITY OF A FINITE SET
Now, consider the following finite sets :
A = {1, 2, 4}; B = {6, 7, 8, 9, 10}; C = {x : x is a alphabet in the word "INDIA"}
Here,
Number of elements in set A = 3.
Number of elements in set B = 5.
Number of elements in set C = 4 (In the set C, the element ‘I’ repeats twice. We know
that the elements of a given set should be distinct. So, the number of distinct elements in set C
is 4).
The number of elements in a finite set is called the cardinal number of the set or the
cardinality of the set.
The cardinal number or cardinality of the set A is denoted as n(A) = 3.