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 :-)

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- December 17th 2008, 03:26 AMJohn GQestion in set theory
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 :-) - December 17th 2008, 01:28 PMPlato

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, .

by

Then show that is injective.