elements of this set is not finite since there are infinite number of natural numbers. We say that the set of natural numbers is an infinite set. The sets A, B and C given above are finite sets and n (A) = , n (B) = and n (C) = some finite number. Definition A set which is empty or consists of a definite number of elements is called finite otherwise, the set is called infinite .
Consider some examples : Let W be the set of the days of the week. Then W is finite. Let S be the set of solutions of the equation x – = . Then S is finite.
(iii) Let G be the set of points on a line. Then G is infinite. When we represent a set in the roster form, we write all the elements of the set within braces { }. It is not possible to write all the elements of an infinite set within braces { } because the numbers of elements of such a set is not finite.
So, we represent SETS some infinite set in the roster form by writing a few elements which clearly indicate the structure of the set followed ( or preceded ) by three dots. For example, { , , . . .} is the set of natural numbers, { , , , , .
. .} is the set of odd natural numbers, {. . .,– , – , – , , , , , .
. .} is the set of integers. All these sets are infinite.