# Sumset Of Cantor Set

Discrete Mathematics Level pending

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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