Question: is z isomorphic to q?
Answer: Prove that Z is not isomorphic to Q. Let f:Z → Q such that f(x) + f(y) = f(x+y). ... Since there is no element of Z that gives 1 when added to itself, a ∉ Z, which means that f is not surjective, not bijective, not an isomorphism. Prove that Q is not isomorphic to Qpos (the multiplicative group of positive rationals).