I consider $ A=\{x^* \in X^* : x^*(x)=0 \} $
$X$ is an abitrary set with its dual space $X^*$.
Why can I say for example, that $x^* \in \mathbb{R^n}$
I thougt, $x^*$ is a functional, such that $$x^* : \mathbb{R^n} \rightarrow \mathbb{R}$$ Didn' t it have to be $$x^* \in \mathbb{R^n}^*$$