It's a trivial fact that the natural numbers are colsed under exponentiation, i.e. x^y is natural for every couple of naturals x,y.
If I start from the positive rationals and add all powers iteratively, I definetly stay inside the positive reals. I think the resulting set contains the algebraic numbers but it is still countable. what else can be said about this set?
Is there some field in mathematics that generalize these questions?