L is the set of cofinite subsets of N (i'm not sure if i understand the concept of cofinite sets).
I need to prove that L is countable. How do i prove this? What to do?
Thanks for any kind of help :-)
I will assume that the positive integers.
A cofinite set has the property that its complement is finite.
Thus each finite subset of corresponds to a cofinite subset of .
The collection of finite subsets of is a countable set.
Lets say that is collections of finite sets, define a mapping from to as follows.
Make a listing of the prime numbers, .
Then show that is injective.