

What is greater: e^pi or pi^e? Six ways to solve this w/o a calculator - strategy
http://mindyourdecisions.com/blog/2013/08/05/monday-puzzle-what-is-greater-epi-or-pie/#.UgBWRZKsjTo

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Millennium
I don't know how you'd prove this, but is it not true that for any real
numbers, if 2 <= x < y, then y^x < x^y?

Again, I don't know how exactly to prove this, so I could be wrong. But this
seems like the most intuitive way to solve something like this: e < pi, so
pi^e < e^pi.

~~~
dalke
It is not true:

    
    
        >>> x = 2.1
        >>> y = 2.2
        >>> y**x < x**y
        False
    
        >>> x = 9.0
        >>> y = 10.0
        >>> y**x < x**y
        True

~~~
Millennium
Oh, OK then. Good to know. Thanks.

