On 9 Jun 2006 14:33:13 -0700, firstname.lastname@example.org wrote:
>Hi everyone, > >I'm having trouble starting the proof that the complex field is not >ordered. I understand the definition of order: > >Suppose F is a collection of numbers, and there is a subset of F, >called P which is closed under addition and miltiplication, so that for >each f in F exactly one of three this is true: 1) f ? P 2) -f ? P >3) f=0. Then we say that F is ordered. > >Now, I honestly don't know where to start in proving that there is no >such set P in complex numbers to do that.
Consider the number i. You will need some additional results you may or may not already have proven.