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

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

2008-03-21

arxiv.org/abs/0803.3119v1

Mathematics

General Mathematics

7 pages

Scientific paper

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.

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