1||0|111|0|
0|0|0|||||Error in the comparing imaginary numbers page|Chris|1|10:48:40|02/23/2007|In the page that talks about comparing imaginary numbers %28%5Burl%5Dhttp%3A%2F%2Fwww.cut-the-knot.org%2Fdo_you_know%2Fcomplex_compare.shtml%5B%2Furl%5D%29 you mention and example where -1%3C1%2C you multiply by i%2C then i again and you get 1%3C%28-1%29 -but by multiplying by i twice you are forgetting your inequality rules- you must switch the less than sign to be more then%3A ergo 1%3E%28-1%29 and the property holds.  Be careful.
1|1|0|||||RE%3A Error in the comparing imaginary numbers page|alexb||11:00:35|02/23/2007|No%2C there is no error.%0D%0A%0D%0AWith the reals you expect%0D%0A%0D%0A%281%29 a %3C b and 0 %3C c imply ac %3C bc.%0D%0A%0D%0AWith the complex numbers%2C either assumption%0D%0A%0D%0A0 %3C i or 0 %3C -i%0D%0A%0D%0Aleads to a contradiction if %281%29 is assumed to work in the complex case as well. Because%2C as you point out%2C i%5Bsup2%5B%2Fsup%5D %3D -1. Which leads to a change of direction in the inequality. The trouble is this direction change is not implied by %281%29.