My problem: Prove that a set of vectors $S$ is linearly independent if and only if any finite subset of $S$ is linearly independent.
I tried like this:
Suppose S is LI.Then the vector $0$ cannot be expressed as a linear sum of all elements of $S$.
How it follows that a finite subset is also LI from this fact. I think $S$ can be finite or infinite.
This is a question from the book Linear Algebra - Friedberg et al.