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In summary, the Cantor set can be seen as a model for an infinite series of coin tosses, with the elements of the set representing sequences of heads and tails. By using a base-3 representation, the Cantor set can be easily mapped to a sequence of coin tosses. However, the ternary numbers containing 1's in this model do not have a clear interpretation.

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[tex]f:C\rightarrow \{0,2\}^\mathbb{N}: 0.a_1a_2a_3...\rightarrow (a_1,a_2,a_3,...)[/tex]

with inverse

[tex]f^{-1}:\{0,2\}^\mathbb{N}\rightarrow C:(a_n)_n\rightarrow \sum_{k=1}^{+\infty} a_k 3^{-k}[/tex]

So more practically, given an element of the Cantor set ##C##, we can see this as a sequence of coin tosses by looking at the base-3 representation. The number ##0.0202020202...## is an element of the Cantor set and corresponds to the sequence ##HTHTHTHTHTHT...##.

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They don't really have an interpretation.

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