- #1
corey115
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Homework Statement
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.
Homework Equations
The axioms for fields and vector spaces.
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?