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Topic: Can anyone help me prove that the complex field is not ordered?
Replies: 16   Last Post: Jun 10, 2006 10:32 PM

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 Toni Lassila Posts: 536 Registered: 12/13/04
Re: Can anyone help me prove that the complex field is not ordered?
Posted: Jun 9, 2006 5:44 PM

On 9 Jun 2006 14:33:13 -0700, mia.mujezinovic@gmail.com 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.