Sumset Of Cantor Set

Probability Level 2

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

C + C \mathcal{C} + \mathcal{C} strictly contains [ 0 , 2 ] [0,2] C + C \mathcal{C} + \mathcal{C} equals [ 0 , 2 ] [0,2] [ 0 , 2 ] [0,2] strictly contains C + C \mathcal{C} + \mathcal{C}

Sameer Kailasa by Sameer Kailasa , 25, USA

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