"pi" can be replaced by any number
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... by any number greater than zero, otherwise x^e is complex ;) Although of course for x < 0 it still holds that Re{e^x} > Re{x^e}
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The difference is close for Pi, but is positive for any positive. Here are some contours for x^y-y^xpic.twitter.com/iX28K5KT7G
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positive for any positive *number* (other than e, obviously); from the same proof. Plotted, e^x-x^e goes like this:pic.twitter.com/xPP0xVQQdz
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Nice you could just use the fact that x >= e on the interval [e,pi] and the integral definition of natural log.pic.twitter.com/xJa9H3UjPp
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There is nothing more elegant than a math proof.
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Are you a mathematician? :O
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Tbh: By saying e*ln(π)=3,1116 you could have "proofed" the proposition by using a calculator from the beginning.
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