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) ----------------------------------------------------------------- gopher://quux.org/ conversion by John Goerzen of http://communication.ucsd.edu/A-News/ This Usenet Oldnews Archive article may be copied and distributed freely, provided: 1. There is no money collected for the text(s) of the articles. 2. The following notice remains appended to each copy: The Usenet Oldnews Archive: Compilation Copyright (C) 1981, 1996 Bruce Jones, Henry Spencer, David Wiseman.