Jonathan - Keith's proposed concept of \\(\le\\) in #4 seemed clear to me: given two points in the complex we say \\(z \le z'\\) if \\(z\\) is closer to the origin than \\(z'\\), i.e.

\[ |z| \le |z'| .\]

This defines a preorder, not a partial order. So my next question was: does this make \\((\mathbb{C}, +, 0) \\) into a monoidal preorder?

(I know the answer; I'm just seeing if he checked the compatibility of this concept of \\(\le\\) with addition.)

\[ |z| \le |z'| .\]

This defines a preorder, not a partial order. So my next question was: does this make \\((\mathbb{C}, +, 0) \\) into a monoidal preorder?

(I know the answer; I'm just seeing if he checked the compatibility of this concept of \\(\le\\) with addition.)