[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)\\).

> 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)\\).