Talk:There exist irrational a and b such that a^b is rational

I'm actually in favor of leaving the cases (noting that the old cases were reversed). We could keep this part, but I'm hesitant to make the proof dependent on something we don't have a proof for on the site. --cynic 15:02, 12 July 2008 (UTC)

Philosophically, I agree with you. On the other hand, the proof by cases is unnecessary when one of the cases is vacuous. The problem was that I posted it with the intention of using the proof by cases, and then later learned about the theorem. I'll post both proofs in an effort to satisfy all of my concerns. - Josh.Manzer