  In the following text for arbitrary $X$ with at least two elements, nonempty
set $\Gamma$ and self-map $\varphi:\Gamma\to\Gamma$ we prove the
set-theoretical entropy of generalized shift $\sigma_\varphi:X^\Gamma\to
X^\Gamma$
($\sigma_\varphi((x_\alpha)_{\alpha\in\Gamma})=(x_{\varphi(\alpha)})_{\alpha\in\Gamma}$
(for $(x_\alpha)_{\alpha\in\Gamma}\in X^\Gamma$)) is either zero or infinity,
moreover it is zero if and only if $\varphi$ is quasi-periodic. We continue our
study on contravariant set-theoretical entropy of generalized shift and
motivate the text using counterexamples dealing with algebraic, topological,
set-theoretical and contravariant set-theoretical positive entropies of
generalized shifts.
