Where can I find the proofs of the properties of exponentiation when powers are members of ℕ, ℤ, ℚ, ℙ, and ℝ?
So far, I have only found this:
http://andrusia.com/math/preliminaries/ExponentiationTheorems.pdf
But I think this only works for exponents that are members of ℕ, and I don't even know if what is offered in that document is an explanation more than a proof, since they should be proven using induction and not ellipsis "..." . Do you consider these are correct proofs?
On the other hand I haven't been able to find over the internet the proofs for exponents members of ℤ, ℚ, ℙ, and ℝ (where ℙ = ℝ\ℚ, to clarify what ℙ is).
Do you know where can these proofs be found?
Thanks in advance.