I just started on Hilbert spaces and found the following exercise:
Let $V$ be a vector space with inner product that has a complete and finite orthonormal set $\{x_1,\dots, x_n\}$. Show that $V$ is finite dimensional
Here what came to my mind: I know that every vector space with finite dimension with an inner product has an orthonormal base, but is the reciprocal true? if it is, then i just have to show that the given orthonormal set is a base?
Any tips will be appreciated. Thanks in advance.