Numerical : Write the set A = { 1 , 4 , 9 , 16 , 25 , . . . } in set-builder form .
Solution : Number 1 , 4 , 6 , 16 , 25 .. are squares of natural numbers 1,2 , 3,4 , 5 etc ..
Therefore set ={ x : x is a square of N }
Empty or null or void set
Set which does not contain any element is called the empty set or the null set or the void set . The empty set is denoted by the symbol φ or { }.
Examples of empty sets . Let A = { x : 5 < x < 6 , x is a natural number }. Then A is the empty set , Thus we dente A set by the symbol φ or { }.
Please note that A = { x : 5 < x < 6 , x is a real number } is not empty set , as there are many real number between 5 & 6 .
Finite & infinite set
A set which is empty or consists of a definite number of elements is called finite otherwise , the set is called infinite .
E . g . A = { 1 , 2 , 3 , 4 , 5 } Finite : n ( A )= 5 . B = { all natural numbers } n ( S ): number of distinct elements Examples of infinite & finite set :
In-finite : n ( B )= infinite
1 . Let W be the set of the days of the week . Then W is finite . 2 . Let G be the set of points on a line . Then G is infinite . 3 . Let A be set of rats in India , then A is infinite . 4 . Let B be set of months in a year , then B is finite . 5 . Let P be set of all prime numbers , the P is infinite .