So I have a final tomorrow and I have no clue how to determine whether a set is vector space or not. I've looked online on how to do these proofs but I still don't understand how to do them. Can any one help me with a question like this?
Let V be the set of all positive real numbers. Determine whether V is a vector space with the operations below.
$x + y = xy$
If it is, verify each vector space axiom; if not, state all vector space axioms that fail.
Edit: Turns out I'm going to fail the exam based on what you guys are saying.