Show that all irreducible representations of a finite group are finite dimensional. We know for any representation $V$ of a finite group $G$, there is a decomposition $V=V_1 \oplus V_2 \oplus.....\oplus V_n$ where $V_i$ s are all irreducibles. Now if we make $V$ irreducibles then just one $V=V_1$(say) will be there. But how can we show $V$ is finite dimensional?
Any help will be apreciated..