the question is:
The relation $<$ is not definable in structure $\langle\mathbb R,+,0\rangle$ with a first order formula.
I asked my professor for help and he told me to consider $\langle\mathbb R,+,0\rangle$ as a vector space and work on its automorphism.
But even now I can't solve this problem...
Can someone please give me some help to understand the clue?
And also why I can't instead prove: the relation $<$ is not definable in the structure $\langle\mathbb N,+,0\rangle$ as a first order formula?