Determine which order axioms are satisfied for a given “pseudo” ordering on the complex numbers

by RoRi

February 25, 2016

Consider a “pseudo-ordering” on the complex field defined by saying a complex number $z = x +iy$ is positive if and only if $x > y$ . Which of the three order axioms (listed in the previous exercise) are satisfied.

The first axiom fails. Take $z = 2 + i$ is positive since $2 > 1$ but $z^2 = 3 + 4i$ is not positive since $3 \not > 4$ .

The second axiom fails since for any $z \neq 0$ such that $x = y$ then neither $z$ nor $-z$ is positive.

The third axiom holds since $0 = 0 + 0i$ implies 0 is not positive.

Stumbling Robot

Determine which order axioms are satisfied for a given “pseudo” ordering on the complex numbers

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