Ahouxn.127
net.math
utcsrgv!utzoo!decvax!duke!chico!harpo!npois!houxi!houxn!gandalf
Tue Mar 16 16:03:49 1982
I=0 paradox
The problem here is going from the step
ln e^2Ipi = ln 1
to
2Ipi=0
It is NOT true that ln e^2Ipi = 2Ipi. ln is a one-to-one function where
it is defined, but e^x is not one-to-one in the imaginary domain. Hence,
they are not inverse functions and the step mentioned above is not valid.
I belive the following to be true:
ln x = ln y iff x=y
if x=y then e^x=e^y
if e^x=e^y then x=y is NOT true (in the domain of both real and imag. )
if ln x=y then e^y=x
if e^y=x then ln x =y is NOT true
I hope this is at least semi-clear.
Monty Estis & Clark Petrie (BTL)
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