For binary operations, NaN values compare as unordered.

The IEEE 754 Specification requires that >,<,= evaluate to False.

Saying that two incomparable objects become comparable let alone gain equally would break things.

We use specific exponents and significands to represent NaNs but they have no numerical meaning.

I am actually surprised python got this correct, often NaN behavior is incorrect out of convenience and causes lots of issues and side effects.