devotion & mathematics

Perfect Number :     A number n is called a perfect number if the sum of all divisors of n > 1 , is equal to 2n.      For example :             Let n = 28.                  The divisors of 28 are 1,2,4,7,14,28.                 Also the sum of these divisors = 1+2+4+7+14+28                                                                   = 56                                                                  = 2 x 28                             ...

  COUNTABLE SETS :-     Consider N, the set of all +ve integers. Any set A is called countable of ∃ a bijection between A and N. Examples :-                                                        1. The set Z of all integers is countable. 2. The set N of all +ve integers is countable. 3. The set Q of all rational numbers is countable. 4. The set of elements {(1/n) / nεN} is countable. 5. The set of all even +ve integers is countable. 6. The set of all odd +ve integers is countable. Properties of countable sets :-  1. Any subset of a countable set is countable. 2. Any subset of N is countable. 3. Union of a finite number of countable sets is countable. 4. A union of countable sets is countable. Atmost countable sets :   A set which is either finite or countably infinite is called atmost countable. properties:-  1....