Let $T$ be a process defined on compact of 2 - adic numbers. $T(x) = x + 1$. 2-adic numbers can be represented as binary number $ x = \sum_{k=0}^{\infty} x_k*2^k$. In this case, the transformation $T$ is given by $ T(1,\dots ,1,0,X_{k+1},X_{k+2},\dots )=(0,\dots ,0,1,X_{k+1},X_{k+2},\dots)$. I need to proof that topological entropy of process $T$ is equaled to $0$ : $h_{top}(T) = 0$. I understand that one-sided generator has entropy 0 for an invertible transformation (knowing the elements of $T^{−1}ξ,T^{−2}ξ,…$ that a given $x$ is in will allow us to completely determine $x$ and in particular know $x's$ position in $ξ$), but I don't know how it can be strictly proofed.
Thank you in advance.