Let $E$ a Banach space with $dim(E)=\infty$ and $B=\{x_{i} \ : \ i\in I\}$ algebraic basis of $E.$ Show that there is at most a finite number of functionals $x^{*}_{i}$ are continuous.
Well, to start with, I already have that $I$ is non-countable and I think we should use Baire's Theorem. Could someone give me a hint?
