This formula is well-defined, since every member of the Cantor set has a ''unique'' base 3 representation withthat only contains the digits 0 or 2,. although in(For some casesmembers of <math>\mathcal{C}</math>, the ternary expansion terminatesis repeating with repeatingtrailing 2's (e.gand there is an alternative non-repeating expansion ending in 1. For example, 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 also holds for all <math>x\in[0,1]\setminus\mathcal{C}</math>.
