Let $\mathcal{C} + \mathcal{C}$ denote the sumset of the Cantor set$\mathcal{C}$. That is, $\mathcal{C} + \mathcal{C} = \{x+y \, : \, x, y \in \mathcal{C}\}.$ Which of the following statements is true about $\mathcal{C} + \mathcal{C}$?

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