I'm trying to define a vector space over Q. Does this make any sense?
The properties of a vector space
The Attempt at a Solution
Let V=Q^2 over Q. It seems to me that everything would be defined and I shouldn't be able to do anything to a vector in this space to make it become an irrational or anything else that could let it step outside the field, so all the axioms of a vector space should hold.
This is the first class I've taken that actually deals with proofs, and I'm not following along too well. I was just wondering if you could do this. It seems quite similar to something like, Let V=R^2 over R.
So if I have something wrong here or make completely no sense, help would be appreciated. Thank you!