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:<math>c(x) =\begin{cases}
\sum_{n=1}^\infty \frac{a_n}{2^n}, & x = \sum_{n=1}^\infty
\frac{2a_n}{3^n}\in\mathcal{C}
\\ \sup_{y\leq x,\, y\in\mathcal{C}} c(y), & x\in [0,1]\setminus \mathcal{C}.\\ \end{cases}
</math>
This formula is well-defined, since every member of the Cantor set has a base 3 representation with only the digits 0 or 2, although in some cases, the ternary expansion terminates with repeating 2's (e.g. 1/3 = 0.1<sub>3</sub> = 0.02222...<sub>3</sub> is a member of the Cantor set). Since ''c''(0) = 0 and ''c''(1) = 1, and ''c'' is monotonic on <math>\mathcal{C}</math>, it is clear that 0 ≤ ''c''(''x'') ≤ 1 for all <math>x\in[0,1]\setminus\mathcal{C}</math>.
==Properties==
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