Nil(Nil(R) = Nil(R) meaning

Question

I was given the exercise to show that Nil(Nil($R$) = Nil($R$), where $R$ is a ring.

Is $x \in$ Nil(Nil($R$)) equivalent to $\exists n, m$ s.t. $x^{n^m}=0$?

I am having a bit of trouble visualising with this notation.

Thanks

Answer 1

It looks like you are overthinking things.

I guess you have been given the definition that for a commutative ring $R$, $Nil(R)$ is the set of nilpotent elements of $R$.

Is it that hard to see what the nilpotent elements of $Nil(R)$ are ?