Set-theoretical entropies of Euler's totient function and other number theoretical special functions

In the following text we show set--theoretical entropy of Euler's totient function and contravariant set--theoretical entropy of Dedekind psi function are zero. Also contravariant set--theoretical entropy of Euler's totient function and set--theoretical entropy of Dedekind psi function are $+\infty$. We pay attention to some of the other number theoretical special functions too. We continue our studies on Alexandroff topologies induced by Euler's totient function and Dedekind psi function.