SOLUTION: Why does the Trichotomy Property not apply to all complex numbers? Thank you

Question 42031: Why does the Trichotomy Property not apply to all complex numbers?
Thank you
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Because the complex number system does NOT have an order relationship. Notice that the real numbers can be arranged on a numberline, so they can be placed in ORDER. Therefore, when comparing real numbers, each number on a real numberline must be equal to, greater than, or less than any other number. Since complex numbers cannot be "arranged in order, there are no such comparisions, and the Trichotomy Property does not apply.

R^2 at SCC
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