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

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