Real Numbers to Irrational Powers

Some examples:

• Eulers Identity $e^{i \pi} + 1 = 0$

• Gelfond-Schneider Constant: $2^\sqrt{2} = 2.66514414269022518865\cdots$ is trancendental by Gelfond-Schneider.

• $i^i = 0.2078795763507619085469556198\cdots$ is also trancendental

• Ramanujan constant: $e^{\pi \sqrt{163}} = 62537412640768743.999999999999250072597\cdots$.

• $e^\gamma$ where $\gamma$ is the Euler–Mascheroni constant. (okay nobody has proved it's irrational yet, but surely is)

Forgive my lack of knowledge of how to correctly implement equations in TeX! I always particularly liked that...

$e^{\pi} - \pi = 19.9990999791894757672664\cdots$

I think it would also be possible to prove that result is transcendental as well. The two cases being $e^{\pi}$ is transcendental or $e^{\pi}$ isn't. The difference of a non-transcendental number and a transcendental number is transcendental, and the only time the difference of two transcendental numbers wouldn't be transcendental is when you could extract the second from the first - That is to say, you could find some non-transcendental $x$ that would satisfy $e^{\pi} = x + \pi$

Unfortunately, my formal proof skills are not what they once were. I'm sure this is trivial, and really the result isn't even that close to 20. But I always liked it :)