I understand that Python really likes things to be comparable with
"<", but from a mathematical point of view the following makes me
cringe:

sage: C.<i>=ComplexField()
sage: 1+i > 1-i
True
sage: 1+i < 1-i
False

Imagine being shown this by a student after you have explained your
complex variables class that complex numbers do NOT have an ordering.

Convincing the student that Sage is being non-mathematical here
requires some work, because sage's choice of comparing first the real
part and then the imaginary part is actually quite a smart one.

Would it break Python too much if comparison would simply throw an
exception in these cases?

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