$K$ : Cantor set
$\phi$ : $K \to [0,1]$, given by $\sum_{k=1}^{\infty} \dfrac{2\epsilon_k}{3^k} \mapsto \sum_{k=1}^{\infty} \dfrac{\epsilon_k}{2^k} \ (\epsilon_k=0,1)$
I hear that this function is increasing, but I don't understand why.
Probably, I have to see $x,y \in K, x<y \Rightarrow \phi(x)<\phi(y)$.
Why does this hold? I would like you to explain.