[Maria wrote in #6](https://forum.azimuthproject.org/discussion/comment/18073/#Comment_18073):
> Let us consider, for example, \$$|z_1|\le |z_2|\$$.

I am not sure this works.

If we define \$$x \preceq y \iff |x| \leq |y|\$$, then we have \$$1/2 \preceq 1\$$ and \$$-1 \preceq -1\$$, but sadly **not** \$$1/2 + (- 1) \preceq 1 + (-1)\$$. This is because \$$|1/2 + (- 1)| = |1/2|\$$ so \$$0 \prec 1/2 + (- 1)\$$.