neat things about e

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lets post some neat things about e!
not the obvious stuff like d[e^x]/dx=e^x but like interesting stuff like how e has the biggest root of itself. like the eth root of e, e^(1/e) is the max of x^(1/x). or how it pops up in compound interest (Pert ) or why e^(i*pi)+1=0

Not true. Try x = -1/2.

By "pops up in compound interest" I take it you refer to limit(m->inf) (1+z/m)^m=e^z.

e = 1/(1-1/(1+1/(2-1/(3+1/(2-1/(5+1/(2-1/(7+1/(2-1/9+1/2-...

oh, i didn't even think of that. so yeah... add ;x>0 to what i said

There again, we could have e = 1.602 176 53(14) × 10^-19 C or e = 4.803 × 10^-10 statcoulombs.

Cheating even more, E as the coefficient of y in the quadratic equation for a conic section.

And again, almost contrapuntal, a book is known, nominally simply "E", which, on passing that, in its titular position, had no occasion for showing any instantiation of that fifth alpha iconic form at all in any word within it.