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+--- Thread: Euler's deamon (/showthread.php?tid=1041)
Euler's deamon - tommy1729 - 12/02/2015
I call this " paradox " Euler's deamon.
It's as annoying as Maxwell's deamon in thermodynamics but for tetration / power towers.
A special case of euler's formula
Exp(a + b i) = exp(a)(cos(b) + sin(b) i)
Gives
e^2pi i = 1.
Now consider
e^2pi i ^ 2pi i = 1 ^ 2pi i = 1
=>
e^(2pi i)^2 = 1 = e^-4 pi^2.
Exp(-4 pi^2) = 1 ??
No division by 0.
No limit.
Not of the form (1^a)^1/a = 1.
( branches !)
Seems like a forward computation.
Terrible.
A true deamon.
Regards
Tommy1729