## Suggestion

$e^\pi> \pi^e.$

How would we go about convincing someone that this amazing inequality is true?

There are several ways to get a feel for this inequality, here are some suggestions:

1. what do the functions $e^x$ and $x^e$ look like?
2. how could we approximate $e$ and $\pi$?
3. do we know any functions that change a question about indices into a question about something else?

How do we define $e^\pi$ and $\pi^e$ given that both numbers are transcendental?