I'm doing some pre-term reading and I've come across direct sums which I'm having a bit of trouble getting my head around.
If V is a vector space and U is a proper subspace (non trivial), I'm told that there are infinitely many different subspaces W of V such that V=U(+)V
[ I've used (+) as the sign for direct sum as i'm not sure how to get it on my computer].
I don't really understand this, and would have no idea on how to prove it. The notes I'm reading hint at thinking about what happens with V is 2-dimensional. Any clues and help would be appreciated!