Proposition: Complex Numbers Cannot Be Ordered
The field of complex numbers is not ordered, i.e. there is no (!) order relation "$\ge$" such that for complex numbers $z_1,z_2,z_3\in\mathbb C$
- from $z_1\ge z_2$ it would follow $z_1+z_3\ge z_2+z_2$ and $z_1$ and
- from $z_1\ge 0$ and $z_2\ge 0$ it would follow that $z_1\cdot z_2\ge 0.$
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