Sets

Countable and Uncountable Sets

A set which is either finite or denumerable is said to be countable
otherwise it is uncountable denumerable is also known as countably
infinite.
Example :The set Z of all integers is countably infinite the function
F : Z -- Z + defined by
f (x) =2n if n > 0
=2n +1 if n <=0
is a bijection.
THEOREM ::
1. Every infinite subset of a countable set A is countable,
2. A countable union of countable sets is countable,
3. A finite product of countable sets is countable.