12/02/2015, 12:50 AM

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

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