The discussion revolves around whether an irrational number raised to an irrational power can yield a rational result. The original poster presents a specific case involving \( A = (\sqrt{2})^{\sqrt{2}} \) and explores the implications of whether \( A \) is rational or irrational.
The discussion is ongoing, with participants sharing opinions and questioning the validity of their reasoning. Some suggest specific cases and explore the beauty of the mathematical concepts involved, while others express uncertainty about the proof of \( A \)'s irrationality.
Participants note that the problem may not have a straightforward solution and that the textbook does not provide answers to even-numbered problems, which adds to the complexity of the discussion.
Ah, yes, let me edit. Edit: Edited.PeroK said:Or, perhaps, ##3^{p/q} = 2##?