Mathematical Science Algebra Polynomial Rings and Irreducibility Criteria

Let ℤ[X] be the ring of polynomials over integers. Then the additive group ℤ[X] is 

1
isomorphic to the multiplicative group ℚ+ of positive rational numbers.
2
isomorphic to the group of rational numbers ℚ under addition
3
countable
4
uncountable

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