The property of the set of the real numbers generated by a   Gelfond-Schneider operator and the countability of all real numbers
  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. 
Slavica Vlahovic and Branislav Vlahovic