R/Multiplication with small a/Nilpotent/Exercise

Let ${}a\in \mathbb {R}$ be a real number with ${}\vert {a}\vert <1$. As is known from analysis, we have

${}\lim _{n\rightarrow \infty }a^{n}=0\,.$

Is the linear mapping

$\mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto ax$

nilpotent?

Create a solution