Alex wrote:

> Anyways, using the bullet-proof method of imagining parallelograms sliding around on the surface of a 3D plot, I think a superset of Matthew's set of solutions is

> $x \preceq_{p,F} y \iff F(p \cdot x) \leq F(p \cdot y)$

> for each point \$$p \in \mathbb{C}\$$ and monotone function \$$F : \mathbb{R} \to \mathbb{R} \$$. I think this is \$$2^{2^{\aleph_0}}\$$ solutions.

How does the function \$$F\$$ affect \$$\preceq_{p,F}\$$? For example, \$$F(x) = 2x\$$ gives the same partial order as \$$F(x) = e^x \$$.