Comment on Closure of exponentiation of real algebraic numbers.
ns1@feddit.uk 2 months ago
Fun question! I don’t know the answer other than to say it’s not just the algebraics because of the Gelfond-Schneider constant
Are you sure this is well-defined? You say that a and b are algebraic but “closure” implies that they could also be any members of S. This might mess up your proof that it’s not all the reals if you do mean the closure.
Ad4mWayn3@sh.itjust.works 2 months ago
My mistake, in that case it’s not the closure what I mean. But then how are those kinds of sets called?
ns1@feddit.uk 2 months ago
You could say something like “the image of exponentiation over…” to mean the set of values created by applying the function once, but it sounds slightly clunky.
Looks like there aren’t really very many sets of mostly transcendental numbers that have names. Computational numbers and periods are two of them, I’d guess that both probably contain your set, so you could compare with those to see where it gets you.