Prove: If $V_1, V_2, ...$ are finite dimensional subspaces of a Vector Space $V$, then for $n = 1, 2, ...$ $V_1 +...+ V_n$ is a finite dimensional subspace of V.
- I have the base case
- I assume true in the induction step.
I don't know what to consider about another finite dimensional subspace $V_{n+1}$
I have a gut-feeling that this is one of those "break off pieces" and then put it all back together induction proof.
Hints Please!