  Considered will be properties of the set of real numbers $\Re$ generated by
an operator that has form of an exponential function of Gelfond-Schneider type
with rational arguments. It will be shown that such created set has cardinal
number equal to ${\aleph_0}^{\aleph_0}=c$. It will be also shown that the same
set is countable. The implication of this contradiction to the countability of
the set of real numbers will be discussed.
