Image and kernel of powers of $\xi$ Let $n$ be a natural integer. Prove that $\xi^n$ is surjective and give a basis of the kernel of $\xi^n$.
\textbf{Image and kernel of powers of $\xi$}\\
Let $n$ be a natural integer. Prove that $\xi^n$ is surjective and give a basis of the kernel of $\xi^n$.