arXiv subjects

Slavica Vlahovic

Publications and source records attributed to Slavica Vlahovic.

3 recordsLinked to original sources

arXiv2008

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.

math.GM↗

arXiv2004

Remarks on Cantor's diagonalization proof of 1891

Remarks on the Cantor's nondenumerability proof of 1891 that the real numbers are noncountable will be given. By the Cantor's diagonal procedure, it is not possible to build numbers that are different from all numbers in a general assumed denumerable sequence of all real numbers. The numbers created on the diagonal of the assumed sequence are not different from the numbers in the assumed denumerable sequence or they do not belong to that sequence.

math.GM↗

arXiv2004

Countability of the Real Numbers

The proofs that the real numbers are denumerable will be shown, i.e., that there exists one-to-one correspondence between the natural numbers $N$ and the real numbers $\Re$. The general element of the sequence that contains all real numbers will be explicitly specified, and the first few elements of the sequence will be written. Remarks on the Cantor's nondenumerability proofs of 1873 and 1891 that the real numbers are noncountable will be given.

math.GM↗