if C {\displaystyle {\mathcal {C}}} is the Cantor set on [0,1], then the Cantor function c : [0,1] → [0,1] can be defined as
is the Cantor set on [0,1], then the Cantor function c : [0,1] → [0,1] can be defined as
![{\displaystyle 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}}\ \mathrm {for} \ a_{n}\in \{0,1\};\\\sup _{y\leq x,\,y\in {\mathcal {C}}}c(y),&x\in [0,1]\setminus {\mathcal {C}}.\\\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/040ba3dfa2d974ebb3210b4cc6b3fa1cb9c9ad97)