In [comment #1](, Matthew Doty found lots of ways we can define \\(\le\\) for complex numbers that make \\((\mathbb{C}, \le, +, 0)\\) into a monoidal poset. However, there are lots of _other_ ways!

A bunch of these are fairly easy to find. You just need to take Matthew's idea and generalize it a little. So, I bet you folks can find them!

There are also a lot of _others_, which are much harder to find. These difficult ones require the axiom of choice. In fact, using the axiom of choice, you can even find nonstandard ways to define \\(\le\\) for _real_ numbers ways that give a monoidal poset \\( (\mathbb{R}, \le, +, 0)\\)!