1. The problem statement, all variables and given/known data Let F be an infinite field (that is, a field with an infinite number of elements) and let V be a nontrivial vector space over F. Prove that V contains infinitely many vectors. 2. Relevant equations The axioms for fields and vector spaces. 3. The attempt at a solution I'm thinking this is easier than I'm making it. Can I say, at the very least, F is countably infinite, so then there exist an infinite amount of scalars to apply to V?