The example z_1 ≹ z_2 for complex numbers z_1, z_2 is weird. Imo it would be clearer to state |z_1| = |z_2|, that is both complex numbers have the same absolute value.

> To conclude, the ≹ symbol plays a crucial role in providing a middle ground between the traditional relational operators.

As a PhD student in math, I have never seen it before. I do not believe that it plays any crucial role.