COUNTABLE, ATMOST COUNTABLE & PERFECT SETS #countable #atmost #perfect #sets #uncountable
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....