A class that implements the rich comparison operators (__lt__, __gt__, __le__, or __ge__) should ensure that all four comparison operations <, <=, >, and >= function as expected, consistent with expected mathematical rules. In Python 3, this is ensured by implementing one of __lt__ or __gt__, and one of __le__ or __ge__. If the ordering is not consistent with default equality, then __eq__ should also be implemented.

Ensure that at least one of __lt__ or __gt__ and at least one of __le__ or __ge__ is defined.

The functools.total_ordering class decorator can be used to automatically implement all four comparison methods from a single one, which is typically the cleanest way to ensure all necessary comparison methods are implemented consistently.

In the following example, only the __lt__ operator has been implemented, which would lead to unexpected errors if the <= or >= operators are used on A instances. The __le__ method should also be defined, as well as __eq__ in this case.

Python Language Reference: Rich comparisons in Python.