Complex numbers and negative roots

  • Thread starter alvin51015
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  • #26
pbuk
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there is no ordering of imaginary numbers.
I'm surprised no one has challenged this!
 
  • #27
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I think the original question has been answered, and continuing this thread does not help.
 
  • #28
HallsofIvy
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There is no indicators of where to put 1 and -1 on the real y axis either. The geometry just seems to be part of an assumptive framework to me, much like rotating counterclockwise and locating the cut. You could really do anything.
The difference is that, while we can "choose" where we put 1 and -1, either choice makes the real numbers an "ordered field". There is NO choice that makes the complex numbers an ordered field.
 
  • #29
HallsofIvy
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I'm surprised no one has challenged this!
We were being kind! Yes, the complex numbers can be ordered but not in such a way as to give an ordered field.
 

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