I want to prove that: 1) $\mathbb{Z}+\mathbb{Z}$ and $\mathbb{Z} + \mathbb{N}$ 2) $\mathbb{Q}$ and $\mathbb{N}\times\mathbb{Q}$ (lexicographical order in $\mathbb{N}\times\mathbb{Q}$) are isomorphic or not.
I know the definition of isomorphic orderings but I don't know how to solve these kind of tasks. Can you give me a hint how to do it correct?