Let {An}n ≥ 1 be a collection of non-empty subsets of ℤ such that An ∩ Am = Ø for m ≠ n. If ℤ = Un ≥ 1 An, then which of the following statements are necessarily true?
1
An is finite for every integer n > 1.
2
An is finite for some integer n ≥ 1.
3
An is infinite for some integer n ≥ 1.
4
An is countable (finite or infinite) for every integer n ≥ 1.