If is a Hamel basis for a vector space with elements, then every subset of having elements are not linearly independent.
Proof:
I am doing this by inductions. I've shown it's true when .
Assume it's true when .
I have trouble with the case when .
Let be a Hamel basis, and be a subset of X. Let be the collection of all linear combinations of .
How do I show that B is not linearly independent?