18 июн. 2014 г. · The Gelfond-Schneider Theorem says that if a and b are algebraic numbers with a≠0,1, and b irrational, then ab is transcendental.

16 мар. 2021 г. · An expository paper on the proof is Gelfond's solution of Hilbert's seventh problem by Carl Einar Hille in American Mathematical Monthly 49 #10 ...

27 февр. 2016 г. · The theorem states that: If a and b are algebraic numbers with a≠0,1 and b non-rational, then any value of ab is a transcendental number.

20 дек. 2017 г. · Its square root 2√2/2 satisfies the same criteria as stated in Gelfond–Schneider theorem, so it is transcendental.

17 авг. 2013 г. · Someone knows a proof (books , articles) that 2 √ 2 is irrational ? Without using that 2 √ 2 is transcendent. Any hints would be appreciated.

22 янв. 2024 г. · Is there an elementary proof that 2√2 is irrational? The Gelfond-Schneider theorem states that if a and b are complex algebraic numbers such ...

11 февр. 2021 г. · The Gelfond-Schneider Theorem actually says: If: α and β are algebraic numbers such that α∉{0,1}; β is either irrational or not wholly real.

16 авг. 2010 г. · If a is an algebraic number other than 0, 1, or -1, then whenever you raise it to an irrational algebraic number, the result is transcendental by the Gelfond– ...

19 окт. 2023 г. · The Gelfond-Schneider Theorem is silent about powers that do not satisfy the hypotheses of the theorem, just like every theorem is silent about ...