Hi.

Could you give me a hint how to solve this problem?

Let $\displaystyle D:= \left\{E \subset \mathbb{R} | 0< card(E)< + \infty \right\} $.

$\displaystyle \phi : D \ni E \rightarrow \sum_{x \in E} \ x \in \mathbb{R}$

Check if $\displaystyle \phi$ is injective or surjective.