In the same way, you can show (I think) that
which is also cool, but not as cool, since "3" is not as cool as "e."
Note: 1/3 < 1/e. This makes sense, since for 0 < x <1, sqrt(x) < cuberoot(x) < fourthroot(x), etc.
Note II: Speaking of e, one of my best friends, a colleague in graduate school (we had the same advisor, and have gotten even closer since), once wrote a paper that contained the number e^e, which I think is about the coolest thing ever published in physics. I wrote about it here for Physics World.